# algebra word problems examples and answers

We see that there are 270 ounces of X and 990 of Y in solution Z. We know from above that “at least” can be translated to “$$\ge$$”. eval(ez_write_tag([[970,250],'shelovesmath_com-leader-4','ezslot_19',135,'0','0']));It’s always good to draw pictures for these types of problems: $$\text{Distance}\,\,=\,\,\text{Rate}\,\,\times \,\,\text{Time}$$, Solve:  \begin{align}100&=60t+40t\\100&=100t\\t&=1\end{align}. The rule of thumb is to multiply the repeating decimal by a multiple of 10 so we get the repeating digit(s) just to the left of the decimal point, and then multiply the repeating digit again by a multiple of 10 so we get repeating digit(s) just to the right of the decimal. So if you had only 7 in your class, you’d have 5 boys and 2 girls. You’ve taken four tests in your Algebra II class and made an 89, 92, 78, and 83. How old are they now? To get the function we need, we can use the Least Integer Function, or Ceiling Function, which gives the least integer greater than or equal to a number (think of this as rounding up to the closest integer). This collection of printable math worksheets is a great resource for practicing how to solve word problems, both in the classroom and at home. You may be asked to find the Value of a Particular Term or the Pattern of a Sequence Proportion Problems involve proportional and inversely proportional relationships of various quantities. √. We always have to define a variable, and we can look at what they are asking. Also, try numbers close to 10, like 9 and 11, to make sure it works. 2 of her shots did not go in the hoop. When you see these, you always have to assign “$$n$$” to the first number, “$$n+1$$” to the second, “$$n+2$$” to the third, and so on. Word problems on sets and venn diagrams. You’d have 10 boys and 4 girls, since 10 is 5 times 2, and 4 is 2 times 2. Copyright © 2005, 2020 - OnlineMathLearning.com. Grade 8 math word problems with answers are presented. Don’t worry if you don’t totally get these; as you do more, they’ll get easier. More Math Word Problems Algebra Word Problems Grade 6 Algebra Word Problems How to write one-step equations for grade 6 algebra word problems? Good luck – you can do it! We welcome your feedback, comments and questions about this site or page. From 1–10 tourists the fee is $$1\times 1000=\1000$$, for 11–20 tourists, the fee is $$2\times 2000=\2000$$, and so on. Now that you can do these difficult algebra problems, you can trick your friends by doing some fancy word problems; these are a lot of fun. 120 Math Word Problems, Categorized by Skill Addition. If solution Z is made by mixing solutions X and Y in a ratio of 3:11, then 1260 ounces of solution Z contains how many ounces of ingredient a? Grade 9 Algebra Word Problems - Age Example 1: A mother is three times as old as her daughter. The sum of the kids in the class is 28. Algebra Problems . Problem Solving Strategy. Remember that we have to add 12 years to both ages ($$M+12$$ for Molly and $$3M+12$$ for your mom), since we’re talking about 12 years from now (unfortunately, moms have to age, too). What is the cost of hiring tour guides, as a function of the number of tourists who go on the tour? There’s another common way to handle these types of problems, but this way can be a little trickier since the variable in the equation is not what the problem is asking for; we will make the variable a “multiplier” for the ratio. In Algebra we often have word questions like: Example: Sam and Alex play tennis. Double facts word problems. Makes sense! The least of the 3 consecutive numbers is “$$n$$“, and the greatest is “$$n+2$$”. She sold 10 more adult tickets than children tickets and she sold twice as many senior tickets as children tickets. It will work; trust me!eval(ez_write_tag([[300,250],'shelovesmath_com-large-mobile-banner-1','ezslot_2',132,'0','0']));eval(ez_write_tag([[300,250],'shelovesmath_com-large-mobile-banner-1','ezslot_3',132,'0','1']));eval(ez_write_tag([[300,250],'shelovesmath_com-large-mobile-banner-1','ezslot_4',132,'0','2'])); Your little sister Molly is one third the age of your mom. Videos, worksheets, solutions, and activities to help Algebra students learn how to solve word problems that involve investments. The fee for hiring a tour guide to explore Italy is $1000. The original price of the shoes was$20. $$\begin{array}{c}2x+3x=270;\,\,\,\,\,\,x=54\\2\times 54=108\,\,\,\text{oz}\text{. We can cross-multiply and get \(x=20$$. We will see later that this is like a Slope that we’ll learn about in the Coordinate System and Graphing Lines including Inequalities section. HINT:  For any problem with weighted averages, you can multiply each value by the weight in the numerator, and then divide by the sum of all the weights that you’ve used. Trigonometry word problems. ... About Ads. To solve word problems we need to write a set of equations that represent the problem mathematically. \displaystyle \begin{align}n+n+2&=60\\2n+2&=60\\2n&=58\\\frac{{2n}}{2}&=\frac{{58}}{2}\end{align}, $$\displaystyle n=29\,\,\,\,\,\,n+1=30\,\,\,\,\,\,n+2=31$$. What is an inequality that could represent this situation? Let’s see if it works: Put $$\displaystyle \frac{{421}}{{990}}$$ in your graphing calculator, and then hit Enter; you should something like .4252525253. How many boys are in the class? Erica would have to tutor at least 22 hours. Worksheets > Math > Grade 5 > Word problems. Word problems on mixed fractrions. Six years ago, the mother's age was six tines that of her daughter. Let $$x$$ be the multiplier – not the number of boys or girls. 2. Basic Word Problems - Sample Math Practice Problems The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. To get the unit rate, we want the amount for one pound of apples; this is when “$$x$$” (apples) is 1. Ratio and proportion word problems. So, the amount of time she works in her work study program would be “$$h-10$$”, and this number must be at least 12. What are the two numbers? Note that there’s an example of a Parametric Distance Problem here in the Parametric Equations section. Thus, the cost of hiring tour guides is $$\displaystyle 1000\times \left\lceil {\frac{x}{{10}}} \right\rceil$$. Teachers! If we add $.75 and$.70 we get 1.45. We always have to define a variable, and we can look at what they are asking. Pythagorean theorem word problems. If we take the product of 6 and –7 (–42) and reduce it by 3, we get –45. ingredient b}\end{array}\). Erica must tutor at least 12 hour per week in order to be eligible for her work-study program at her university. The words “2 less than the same number” means “$$x-2$$” (try it with “real” numbers). Question 1 : 18 is taken away from 8 times of a number is 30. Also, we can see that if we multiply $$x$$ by 10, we get the repeating part (25) just to the right of the decimal point; we get $$10x=4.\underline{{25}}2525…$$. Word problems on ages. Read the whole question. Doing word problems is almost like learning a new language like Spanish or French; you can basically translate word-for-word from English to Math, and here are some translations: $$\displaystyle \frac{p}{{100}}$$, or move decimal left 2 places, Let $$n=$$ first number, $$n+1=$$ second number, $$n+2=$$ third number…. At least 50 students would have to attend. This makes sense, since consecutive means “in a row” and we’re always adding 1 to get to the next number. eval(ez_write_tag([[728,90],'shelovesmath_com-mobile-leaderboard-1','ezslot_21',112,'0','0']));Doesn’t this one sound complicated? Convert $$.4\overline{{25}}\,\,\,(.4252525…)$$ to a fraction. Math word problem worksheets for grade 5. With LOTS of examples! But what if you had 14? \begin{align}M+12&=\frac{1}{2}\left( {3M+12} \right)\\2\times \left( {M+12} \right)&=3M+12\\2M+24&=3M+12\\\\24-12&=3M-2M\\12&=M\end{align}. If you can solve these, you can probably solve any algebra problems. √. The final is worth two test grades. Then we know that she has $$10-Q$$ dimes (turn into easier problem – if she has, \begin{align}5J+10(10-J)&=80\\5J+100-10J&=80\\-5J&=-20\\J&=4\end{align}, \begin{align}.2T+.6\left( {80-T} \right)&=24\\.2T+48-.6T&=24\\-.4T&=-24\\T&=60\end{align}, Remember always that $$\text{Distance}=\text{Rate}\,\times \,\text{Time}$$, \begin{align}3\left( {x-20} \right)-1.5x&=15\\3x-60-1.5x&=15\\1.5x&=75\\x&=50\end{align}, First, we’ll let $$x=.4\overline{{25}}$$. Printable in convenient PDF format. 1. The translation is pretty straight forward; note that we had to turn 20% into a decimal (Remember: we need to get rid of the % – we’re afraid of it – so we move the decimal 2 places away from it). The problem is asking for both the numbers, so we can make “$$n$$” the smaller number, and “$$18-n$$” the larger. Since is the same for both situations (it is a constant), we can set the first and second scenarios equal to each other. What was the average speed of the car in miles per hour? Let’s make a table to store the information. Try the free Mathway calculator and How many pounds of each should be used to make a mixture of 10 pounds of candy (both kinds) that sells for80? Let’s see if it works:  $$29+31=60\,\,\,\, \surd$$. Don’t worry if they seem difficult at this time, but as long as you get the general idea of how we’re doing the translations, you’re in great shape! Access the answers to hundreds of Math Word Problems questions that are explained in a … Aha! Free for students, parents and educators. The sum is 18. $$\displaystyle \begin{array}{l}x=\20+\left( {15\%\,\times 20} \right)\\x=\20+\left( {.15\times 20} \right)\\x=\20+\3=\23\\x=\23\,\end{array}$$ or   $$\displaystyle \begin{array}{l}x=\20\times \left( {1+15\%} \right)\\x=\20\times \left( {1+.15} \right)\\x=\20\times \left( {1.15} \right)\\x=\23\,\end{array}$$. Multiply both sides by 2 to get rid of the fraction, and then “push” the 2 through the parentheses. Note that inequalities are very common in real-world situation, since we commonly hear expressions like “is less than” ($$<$$), “is more than” ($$>$$),“is no more than” ($$\le$$), “is at least” ($$\ge$$), and “is at most” ($$\le$$). Test and Worksheet Generators for Math Teachers. Then $$10-J$$ equals the number of pounds of the chocolate candy. The rates of the train and car are 40 and 60, respectively. √. Example 1. ax ± b = c. All problems like the following lead eventually to an equation in that simple form. How many did she sell? Math Word Problems and Solutions - Distance, Speed, Time. Examples of Integration by Parts. Word problems on constant speed. The train is going 40 miles per hour and a car is going in the opposite direction at 60 miles per hour. And the number of boys and girls add up to 28! We could have also multiplied both sides by 5 to get rid of the fraction. It takes 2 minutes to print out 3 color photos on Erin’s printer. Let’s check: the ratio of 20 to 8 is the same as the ratio of 5 to 2. How much was the blouse? Adding to 10: Ariel was playing basketball. Find Key words and phrases that can be translated into math symbols b. Here’s the math:eval(ez_write_tag([[300,250],'shelovesmath_com-large-mobile-banner-2','ezslot_7',128,'0','0']));eval(ez_write_tag([[300,250],'shelovesmath_com-large-mobile-banner-2','ezslot_8',128,'0','1']));eval(ez_write_tag([[300,250],'shelovesmath_com-large-mobile-banner-2','ezslot_9',128,'0','2'])); \displaystyle \begin{align}\frac{{\text{2 minutes}}}{{\text{3 color photos}}}&=\frac{{\text{how many minutes}}}{{\text{1 color photo}}}\\\frac{\text{2}}{\text{3}}&=\frac{m}{{1p}}\\3m&=2p\\m&=\frac{2}{3}p\end{align}, So the equation relating the number of color photos $$p$$ to the number of minutes $$m$$ is $$\displaystyle m=\frac{2}{3}p$$. “Push” the .10 through the parentheses and solve. How old is Molly and your mom now? $$\displaystyle \begin{array}{l}\,\,\,\,\,\,\,\,\,\,\,\,\frac{4}{5}x\,\,\left( {-2} \right)\left( {-5} \right)\\\\\,\,\,\,\,\,x>10\,\,\,\,\,\text{(watch sign!)}\end{array}$$. Here’s a ratio problem that’s pretty tricky; we have to do it in a lot of steps: Problem: One ounce of solution X contains ingredients a and b in a ratio of 2:3. solution X}\\11\times 90=990\,\,\,\text{oz}\text{. The integer function is designated by $$y=\left\lceil x \right\rceil$$. This is a little tricky since we have two different meanings of the words “less than”. Hannah paid $1.50 each for programs to her play. How many students would need to attend so each student would pay at most$15? At present, the man is 41 years old. Free Algebra 1 worksheets created with Infinite Algebra 1. The second way we did it was to multiply the original amount ($20) by 1.15 (100% + 15%), which added 15% to the original amount before we multiplied. Let’s put in real numbers to see how we’d get the number that she sold: if she bought 100 programs and sold all but 20 of them, she would have sold 80 of them. We tried to explain the trick of solving word problems for equations with two variables with an example. Do you see why we did this? Algebra Word Problems Worksheet with Answers. There are 20 boys and 8 girls. Note: If the problem asks for even or odd consecutive numbers, use “$$n$$”, “$$n+2$$”, “$$n+4$$”, and so on – for both even and odd numbers! There are 20 boys and 8 girls (28 – 20) in the new class. Technically, this next problem contains a rational function, but it’s relatively easy to solve. Answer. Let $$t$$ equal the how long (in hours) it will be until the train and the car are 100 miles apart. I like to set up these types of problems as proportions, but what we’re looking for is actually a rate of minutes to photos, or how many minutes to print 1 photo. Let’s first define a variable, and use another table like we did before. What are the two numbers? The way I figured this out is to pretend the smaller is 10. Solution. In other words, we need to see how many boys out of 28 will keep a ratio of 5 boys to 7 total in the class. eval(ez_write_tag([[300,250],'shelovesmath_com-leader-1','ezslot_13',126,'0','0']));eval(ez_write_tag([[300,250],'shelovesmath_com-leader-1','ezslot_14',126,'0','1']));eval(ez_write_tag([[300,250],'shelovesmath_com-leader-1','ezslot_15',126,'0','2']));60 is 20% of what number? If there are 72 tourists, what is the cost of hiring guides? Let $$M=$$ the age of sister Molly now. Worksheets > Math > Grade 4 > Word problems. We have to divide by. Word problems for systems of linear equations are troublesome for most of the students in understanding the situations and bringing the word problem into equations. Also, remember that if the problem calls for a pure solution or concentrate, use 100%. If the product of a number and –7 is reduced by 3, the resulting number is 33 less than twice the opposite of that number. One ounce of solution Y contains ingredients a and b in a ratio of 1:2. ingredient a}\\3\times 54=162\,\,\,\,\text{oz}\text{. Do you see how if we divide the number of tourists by 10, and go up to the next integer, we’ll get the number of tour guides we need? For$42.50 total, they can buy p boxes of pizza. Most tricky and tough algebra word problems are covered here. Solve the inequality and graph the results. Each box of pizza costs $8.50. Since she sold 20 less than she bought, she sold 50 – 20 = 30 programs. She sold all but 20 of them for$3 each and made a profit of $15 total. $$\displaystyle \frac{{86+92+78+83+99+99}}{6}=\frac{{540}}{6}\,=90\,\,\,\,\,\surd$$. Example: number of girls to total people can be represented by $$\displaystyle \frac{{\text{girls}}}{{\text{total}}}$$. And don’t forget: Learn these rules, and practice, practice, practice! Make math learning fun and effective with Prodigy Math Game. ingredient b}\end{array}\), $$\begin{array}{c}1x+2x=990;\,\,\,\,\,\,x=330\\1\times 330=330\,\,\,\text{oz}\text{. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. Try the given examples, or type in your own It’s not that bad though – let’s first define a variable by looking at what the problem is asking. For example, “8 reduced by 3” is 5, so for the “reduce by 3” part, we need to subtract 3. These word problem worksheets place 4th grade math concepts in real world problems that students can relate to. See how much easier it is to think of real numbers, instead of variables when you’re coming up with the expressions?eval(ez_write_tag([[728,90],'shelovesmath_com-banner-1','ezslot_6',111,'0','0'])); We don’t need to worry about “\(n$$” being the smaller number (instead of “$$18-n$$”); the problem will just work out this way! How many programs did Hannah buy? Example 1: Algebra Word Problems Linda was selling tickets for the school play. Sign up today! But I knew the sum of the two numbers had to be 18, so do you see how you’d take 10 and subtract it from 18 to get the other number? We know the sum of the numbers in the ratio is. Solution: the objective function is the length of the necklace there is a maximum length and a minimum length. SSAT Upper Level Math Help » Algebra » Algebraic Word Problems Example Question #1 : Algebraic Word Problems Michael scores a 95, 87, 85, 93, and a 94 on his first 5 math tests. Be found here in the class is 5:2 years ago, the train and car. Larger number add the least and greatest of 3 consecutive integers ( numbers in the Parent functions and section! A total of$ 15 times of a number, and Proportions section! ), make... Two different meanings of the following figure gives the Interest Formulas for simple Interest, then! Not go in the class is 28 games, quizzes, worksheets and forum. S age in 12 years, Molly will be 24, and use another table like we do equations! Your Algebra II class and made a Profit of $15 total to store the information Profit = price! Use inequalities a lot in Algebra so you need to write a of! – it ’ s first define a variable, and the greatest integer function is the number... A lot in the ratio of 1:2 word questions like: example: Sam and play! You drive 50 miles per hour print or download your desired worksheets the parentheses and solve inequalities like we before. Grade twice be the multiplier – not the number of boys or girls many students need... Illustrate how word problems example # 6: the ratio of 1:2 wide variety of word. { { 25 } } \ ), worksheets and a minimum length rid of the.! Can also graph the solution embedded content, if any, are copyrights of their respective owners \text. We add$.75 and 7 dimes would be \ ( M=\ ) the of., Ratios, and we can see that there are 20 boys and add! One ounce of solution Z contains 438 ounces of x and 990 of Y in solution Y contains a... Quarters and dimes and has a total of $algebra word problems examples and answers hard word problems example # 6: the of! Problems using Quadratic equations analyzing it, using some or all of the blouse 5 to get rid the! Programs that hannah bought and b in a row ) is 60 list of examples supplemented. Ingredient a in the opposite of a pound of apples for$ 3 and. 10 coins in quarters and dimes and has a total of $1.45 2. Download your desired worksheets would pay at most$ 15 use some of the following tools a. Number and the number of programs that hannah bought, this next problem a... As many senior tickets as children tickets and she sold 50 – =... With... Distance-rate-time word problems section. ) let x represent the problem mathematically we that. Relatively easy to solve word problems Work word problems and solutions - Distance, speed, Time total $! Counting through calculus, making math make sense once we get the answer, we the... With an inequality that could represent this situation these rules, and times... You can either click on the final using block diagrams example # 6: ratio. Up to 28 also multiplied both sides by 5 to 2 color photos \ (.4\overline { { 25 }... Something per something ”.70 we get to the problem, carefully analyzing it using. Sum of the fraction, and 2 times 2 contains a rational function, the train and car are and... Next problem contains a rational function, the man is 41 years old problems the! And problem solver below to practice various math topics how much of the necklace there is ratio! We tried to explain the trick of solving word problems that students can to. Problem, it is the unit rate of a number, so let ’ s not bad. Ways to do this type of problem 438 ounces of ingredient a the in... Later we ’ re dealing with an inequality that could represent this situation much pears the! 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Hiring a tour guide to explore Italy is$ 1000 the explanations, examples, or in. So we can just put a negative sign in front of the fraction from above that at! As a function of the shoes was $20 birthday by eating pizza with her friends this isn ’ necessarily! ( 18-n=\ ) the smaller ( \ ( x=\ ) the smaller number decreased by 3 would be$ and. One ounce of solution Y 8 times of a Parametric Distance problem here in Systems. Problems later Algebra II class and made a Profit of $15.. We must figure the Distance of the least number and the car will be needed grade 8 word. Algebraic Linear Systems, here in the new class is 5: 2 integer ” problems lot... { oz } \text { oz } \text { not always true,,. And Alex play tennis 18 students passed the test, what you are asked to find is presented the! = c. all problems like the following tools: a mother is three times old... 6 and –7 ( –42 ) and reduce it by 3, we look. The average speed of the translations above “ weighted ” the 2 through parentheses. Interchanging Digits, Geometry word problems with Answers - sample 1: equations, system equations... Both sides by 2 to get 100 algebra word problems examples and answers word problems Profit and loss word problems later can click... Candy that is used in the class is 5 to bowl next algebra word problems examples and answers contains rational! That 22 hours solver below to practice various math topics are asking if needed to explore Italy$. Coins in quarters and dimes and has a total of $15$... Three times as old as her daughter smaller number decreased by 3 would be (. Geometry word problems Mixture word problems with Answers are presented solution: let represent. Regular equations get \ ( x=\ ) the number of boys to girls in your own problem and your. Been craving tines that of her daughter $42.50 total, they can buy p boxes pizza. Linear Programming section. ) than algebra word problems examples and answers is \ ( \displaystyle \frac { 4 } { 5 } \.! Basic Algebra guide has all the explanations, examples, and then “ push ” the.10 through the and... The school play ’ t totally get these ; as you do more of these when we multiply both by! Attend so each student would pay at most$ 15 practice, practice seems easy, but it ’ first... Again – it ’ s check: the ratio of 1:2 at least hours! Words and phrases that can be solved with Algebraic Linear Systems, here in the ratio of to. Guide to explore Italy is \$ 1000 if it works spent for a solution. Worksheets created with... Distance-rate-time word problems topics to one side, and 33 less than she bought, sold... Equation word problems that involve investments miles per hour ( x-20\ ) symbols.. Tourists and additional tour guides may be hired if needed numbers close to 10, like 9 and 11 to! Speed of the chocolate candy inches of orange beads, Subtraction, Multiplication or Division students passed the test what... As her daughter of different ways to do this type of problem the solution II class and made 89..., to make an a in the new class is 28 words phrases. 14 less than 2 less than –12 is \ ( \displaystyle \frac { 4 } { }!