Word Problems Linear Equations

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$\textbf<1)>$ Joe and Steve are saving money. Joe starts with $105 and saves $5 per week. Steve starts with $5 and saves $15 per week. After how many weeks do they have the same amount of money?

$y= 5x+105,\,\,\,y=15x+5$ 10 weeks ($155)

$\textbf<2)>$ Mike and Sarah collect rocks. Together they collected 50 rocks. Mike collected 10 more rocks than Sarah. How many rocks did each of them collect?

Mike collected 30 rocks, Sarah collected 20 rocks.

$\textbf<3)>$ In a classroom the ratio of boys to girls is 2:3. There are 25 students in the class. How many are girls?

15 girls (10 boys)

$\textbf<4)>$ Kyle makes sandals at home. The sandal making tools cost $100 and he spends $10 on materials for each sandal. He sells each sandal for $30. How many sandals does he have to sell to break even?

$C=10x+100,\,\,\,R=30x$ 5 sandals ($150)

$\textbf<5)>$ Molly is throwing a beach party. She still needs to buy beach towels and beach balls. Towels are $3 each and beachballs are $4 each. She bought 10 items in total and it cost $34. How many beach balls did she get?

4 beachballs (6 towels)

$\textbf<6)>$ Anna volunteers at a pet shelter. They have cats and dogs. There are 36 pets in total at the shelter, and the ratio of dogs to cats is 4:5. How many cats are at the shelter?

20 cats (16 dogs)

$\textbf<7)>$ A store sells oranges and apples. Oranges cost $1.00 each and apples cost $2.00 each. In the first sale of the day, 15 fruits were sold in total, and the price was $25. How many of each type of frust was sold?

$o+a=15,\,\,\,1o+2a=25$ 10 apples and 5 oranges

$\textbf<8)>$ The ratio of red marbles to green marbles is 2:7. There are 36 marbles in total. How many are red?

8 red marbles (28 green marbles)

$\textbf<9)>$ A tennis club charges $100 to join the club and $10 for every hour using the courts. Write an equation to express the cost $C$ in terms of $h$ hours playing tennis.

The equation is $C=10h+100$

$\textbf<10)>$ Emma and Liam are saving money. Emma starts with $80 and saves $10 per week. Liam starts with $120 and saves $6 per week. After how many weeks will they have the same amount of money?

$E = 10x + 80,\,\,\,L = 6x + 120$ 10 weeks ($180 each)

$\textbf<11)>$ Mark and Lisa collect stamps. Together they collected 200 stamps. Mark collected 40 more stamps than Lisa. How many stamps did each of them collect?

$M + L = 200,\,\,\,M = L + 40$ Mark collected 120 stamps, Lisa collected 80 stamps.

$\textbf<12)>$ In a classroom, the ratio of boys to girls is 3:5. There are 40 students in the class. How many are boys?

$B + G = 40,\,\,\,5B = 3G$ 15 boys (25 girls)

$\textbf<13)>$ Lisa is selling handmade jewelry. The materials cost $60, and she sells each piece for $20. How many pieces does she have to sell to break even?

$\textbf<14)>$ Tom is buying books and notebooks for school. Books cost $15 each, and notebooks cost $3 each. He bought 12 items in total, and it cost $120. How many notebooks did he buy?

$B + N = 12,\,\,\,15B+3N=120$ 5 notebooks (7 books)

$\textbf<15)>$ Emily volunteers at an animal shelter. They have rabbits and guinea pigs. There are 36 animals in total at the shelter, and the ratio of guinea pigs to rabbits is 4:5. How many guinea pigs are at the shelter?

$R + G = 36,\,\,\,5G=4R$ 16 guinea pigs (20 rabbits)

$\textbf<16)>$ Mike and Sarah are going to a theme park. Mike’s ticket costs $40, and Sarah’s ticket costs $30. They also bought $20 worth of food. How much did they spend in total?

$M + S + F = T,\,\,\,M=40,\,\,\,S=30,\,\,\,F=20$ They spent $90 in total.

$\textbf<17)>$ The ratio of red marbles to blue marbles is 2:3. There are 50 marbles in total. How many are blue?

$R + B = 50,\,\,\,3R=2B$ 30 blue marbles (20 red marbles)

$\textbf<18)>$ A pizza restaurant charges $12 for a large pizza and $8 for a small pizza. If a customer buys 5 pizzas in total, and it costs $52, how many large pizzas did they buy?

$L + S = 5,\,\,\,12L+8S=52$ They bought 3 large pizzas (2 small pizzas).

$\textbf<19)>$ The area of a rectangle is 48 square meters. If the length is 8 meters, what is the width of the rectangle?

$A=L\times W,\,\,\,L=8,\,\,\,A=48$ The width is 6 meters.

$\textbf<20)>$ Two numbers have a sum of 50. One number is 10 more than the other. What are the two numbers?

The numbers are 30 and 20.

$\textbf<21)>$ A store sells jeans for $40 each and T-shirts for $20 each. In the first sale of the day, they sold 8 items in total, and the price was $260. How many of each type of item was sold?

$J+T=8,\,\,\,40J+20T=260$ 5 jeans and 3 T-shirts were sold.

$\textbf<22)>$ The ratio of apples to carrots is 3:4. There are 28 fruits in total. How many are apples?

There are 12 apples and 16 carrots.

$\textbf<23)>$ A phone plan costs $30 per month, and there is an additional charge of $0.10 per minute for calls. Write an equation to express the cost $c$ in terms of $m$ minutes.

The equation is c=30+0.10m

$\textbf<24)>$ A triangle has a base of 8 inches and a height of 6 inches. Calculate its area.

$A=0.5\times B\times H,\,\,\,B=8,\,\,\,H=6$ The area is 24 square inches.

$\textbf<25)>$ A store sells shirts for $25 each and pants for $45 each. In the first sale of the day, 4 items were sold, and the price was $180. How many of each type of item was sold?

$T+P=4,\,\,\,25T+45P=180$ 0 shirts and 4 pants were sold.

$\textbf<26)>$ A garden has a length of 12 feet and a width of 10 feet. Calculate its area.

$A=L\times W,\,\,\,L=12,\,\,\,W=10$ The area is 120 square feet.

$\textbf<27)>$ The sum of two consecutive odd numbers is 56. What are the two numbers?

The numbers are 27 and 29.

$\textbf<28)>$ A toy store sells action figures for $15 each and toy cars for $5 each. In the first sale of the day, 10 items were sold, and the price was $110. How many of each type of item was sold?

$A+C=10,\,\,\,15A+5C=110$ 6 action figures and 4 toy cars were sold.

$\textbf<29)>$ A bakery sells pie for $2 each and cookies for $1 each. In the first sale of the day, 14 items were sold, and the price was $25. How many of each type of item was sold?

11 pies and 3 cookies were sold.

$\textbf$ Two car rental companies charge the following values for x miles.
Car Rental A: $y=3x+150 \,\,$ Car Rental B: $y=4x+100$

$\textbf<30)>$ Which rental company has a higher initial fee?

Company A has a higher initial fee

$\textbf<31)>$ Which rental company has a higher mileage fee?

Company B has a higher mileage fee

$\textbf<32)>$ For how many driven miles is the cost of the two companies the same?

The companies cost the same if you drive 50 miles.

$\textbf<33)>$ What does the $3$ mean in the equation for Company A?

For company A, the cost increases by $3 per mile driven.

$\textbf<34)>$ What does the $100$ mean in the equation for company B?

For company B, the initial cost (0 miles driven) is $100.

$\textbf$ Andy is going to go for a drive. The formula below tells how many gallons of gas he has in his car after m miles.
$g=12-\frac$

$\textbf<35)>$ What does the $12$ in the equation represent?

Andy has $12$ gallons in his car when he starts his drive.

$\textbf<36)>$ What does the $18$ in the equation represent?

It takes $18$ miles to use up $1$ gallon of gas.

$\textbf<37)>$ How many miles until he runs out of gas?

The answer is $216$ miles

$\textbf<38)>$ How many gallons of gas does he have after 90 miles?

The answer is $7$ gallons

$\textbf<39)>$ When he has $3$ gallons remaining, how far has he driven?

The answer is $162$ miles

$\textbf$ Joe sells paintings. Each month he makes no commission on the first $5,000 he sells but then makes a 10% commission on the rest.

$\textbf<40)>$ Find the equation of how much money x Joe needs to sell to earn y dollars per month.

The answer is $y=.1(x-5,000)$

$\textbf<41)>$ How much does Joe need to sell to earn $10,000 in a month.

The answer is $$105,000$

$\textbf<42)>$ How much does Joe earn if he sells $45,000 in a month?

The answer is $$4,000$

See Related Pages

$\bullet\text< Word Problems- Linear Equations>$
$\,\,\,\,\,\,\,\,$

$\bullet\text< Word Problems- Averages>$
$\,\,\,\,\,\,\,\,$

$\bullet\text< Word Problems- Consecutive Integers>$
$\,\,\,\,\,\,\,\,$

$\bullet\text< Word Problems- Distance, Rate and Time>$
$\,\,\,\,\,\,\,\,$

$\bullet\text< Word Problems- Break Even>$
$\,\,\,\,\,\,\,\,$

$\bullet\text< Word Problems- Ratios>$
$\,\,\,\,\,\,\,\,$

$\bullet\text< Word Problems- Age>$
$\,\,\,\,\,\,\,\,$

$\bullet\text< Word Problems- Mixtures and Concentration>$
$\,\,\,\,\,\,\,\,$

In Summary

Linear equations are a type of equation that has a linear relationship between two variables, and they can often be used to solve word problems. In order to solve a word problem involving a linear equation, you will need to identify the variables in the problem and determine the relationship between them. This usually involves setting up an equation (or equations) using the given information and then solving for the unknown variables
.
Linear equations are commonly used in real-life situations to model and analyze relationships between different quantities. For example, you might use a linear equation to model the relationship between the cost of a product and the number of units sold, or the relationship between the distance traveled and the time it takes to travel that distance.

Linear equations are typically covered in a high school algebra class. These types of problems can be challenging for students who are new to algebra, but they are an important foundation for more advanced math concepts.

One common mistake that students make when solving word problems involving linear equations is failing to set up the problem correctly. It’s important to carefully read the problem and identify all of the relevant information, as well as any given equations or formulas that you might need to use.

Other related topics involving linear equations include graphing and solving systems. Understanding linear equations is also useful for applications in fields such as economics, engineering, and physics.

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Word Problems Linear Equations

\(\textbf<1)>\) Joe and Steve are saving money. Joe starts with $105 and saves $5 per week. Steve starts with $5 and saves $15 per week. After how many weeks do they have the same amount of money?

\(\textbf<2)>\) Mike and Sarah collect rocks. Together they collected 50 rocks. Mike collected 10 more rocks than Sarah. How many rocks did each of them collect?

\(\textbf<3)>\) In a classroom the ratio of boys to girls is 2:3. There are 25 students in the class. How many are girls?

\(\textbf<4)>\) Kyle makes sandals at home. The sandal making tools cost $100 and he spends $10 on materials for each sandal. He sells each sandal for $30. How many sandals does he have to sell to break even?

\(\textbf<5)>\) Molly is throwing a beach party. She still needs to buy beach towels and beach balls. Towels are $3 each and beachballs are $4 each. She bought 10 items in total and it cost $34. How many beach balls did she get?

\(\textbf<6)>\) Anna volunteers at a pet shelter. They have cats and dogs. There are 36 pets in total at the shelter, and the ratio of dogs to cats is 4:5. How many cats are at the shelter?

\(\textbf<7)>\) A store sells oranges and apples. Oranges cost $1.00 each and apples cost $2.00 each. In the first sale of the day, 15 fruits were sold in total, and the price was $25. How many of each type of frust was sold?

\(\textbf<8)>\) The ratio of red marbles to green marbles is 2:7. There are 36 marbles in total. How many are red?

\(\textbf<9)>\) A tennis club charges $100 to join the club and $10 for every hour using the courts. Write an equation to express the cost \(C\) in terms of \(h\) hours playing tennis.

\(\textbf<10)>\) Emma and Liam are saving money. Emma starts with $80 and saves $10 per week. Liam starts with $120 and saves $6 per week. After how many weeks will they have the same amount of money?

\(\textbf<11)>\) Mark and Lisa collect stamps. Together they collected 200 stamps. Mark collected 40 more stamps than Lisa. How many stamps did each of them collect?

\(\textbf<12)>\) In a classroom, the ratio of boys to girls is 3:5. There are 40 students in the class. How many are boys?

\(\textbf<13)>\) Lisa is selling handmade jewelry. The materials cost $60, and she sells each piece for $20. How many pieces does she have to sell to break even?

\(\textbf<14)>\) Tom is buying books and notebooks for school. Books cost $15 each, and notebooks cost $3 each. He bought 12 items in total, and it cost $120. How many notebooks did he buy?

\(\textbf<15)>\) Emily volunteers at an animal shelter. They have rabbits and guinea pigs. There are 36 animals in total at the shelter, and the ratio of guinea pigs to rabbits is 4:5. How many guinea pigs are at the shelter?

\(\textbf<16)>\) Mike and Sarah are going to a theme park. Mike’s ticket costs $40, and Sarah’s ticket costs $30. They also bought $20 worth of food. How much did they spend in total?

\(\textbf<17)>\) The ratio of red marbles to blue marbles is 2:3. There are 50 marbles in total. How many are blue?

\(\textbf<18)>\) A pizza restaurant charges $12 for a large pizza and $8 for a small pizza. If a customer buys 5 pizzas in total, and it costs $52, how many large pizzas did they buy?

\(\textbf<19)>\) The area of a rectangle is 48 square meters. If the length is 8 meters, what is the width of the rectangle?

\(\textbf<20)>\) Two numbers have a sum of 50. One number is 10 more than the other. What are the two numbers?

\(\textbf<21)>\) A store sells jeans for $40 each and T-shirts for $20 each. In the first sale of the day, they sold 8 items in total, and the price was $260. How many of each type of item was sold?

\(\textbf<22)>\) The ratio of apples to carrots is 3:4. There are 28 fruits in total. How many are apples?

\(\textbf<23)>\) A phone plan costs $30 per month, and there is an additional charge of $0.10 per minute for calls. Write an equation to express the cost \(c\) in terms of \(m\) minutes.

\(\textbf<24)>\) A triangle has a base of 8 inches and a height of 6 inches. Calculate its area.

\(\textbf<25)>\) A store sells shirts for $25 each and pants for $45 each. In the first sale of the day, 4 items were sold, and the price was $180. How many of each type of item was sold?

\(\textbf<26)>\) A garden has a length of 12 feet and a width of 10 feet. Calculate its area.

\(\textbf<27)>\) The sum of two consecutive odd numbers is 56. What are the two numbers?

\(\textbf<28)>\) A toy store sells action figures for $15 each and toy cars for $5 each. In the first sale of the day, 10 items were sold, and the price was $110. How many of each type of item was sold?

\(\textbf<29)>\) A bakery sells pie for $2 each and cookies for $1 each. In the first sale of the day, 14 items were sold, and the price was $25. How many of each type of item was sold?

\(\textbf\) Two car rental companies charge the following values for x miles. Car Rental A: \(y=3x+150 \,\,\) Car Rental B: \(y=4x+100\)

\(\textbf<30)>\) Which rental company has a higher initial fee?

\(\textbf<31)>\) Which rental company has a higher mileage fee?

\(\textbf<32)>\) For how many driven miles is the cost of the two companies the same?

\(\textbf<33)>\) What does the \(3\) mean in the equation for Company A?

\(\textbf<34)>\) What does the \(100\) mean in the equation for company B?

\(\textbf\) Andy is going to go for a drive. The formula below tells how many gallons of gas he has in his car after m miles. \(g=12-\frac\)

\(\textbf<35)>\) What does the \(12\) in the equation represent?

\(\textbf<36)>\) What does the \(18\) in the equation represent?

\(\textbf<37)>\) How many miles until he runs out of gas?

\(\textbf<38)>\) How many gallons of gas does he have after 90 miles?

\(\textbf<39)>\) When he has \(3\) gallons remaining, how far has he driven?

\(\textbf\) Joe sells paintings. Each month he makes no commission on the first $5,000 he sells but then makes a 10% commission on the rest.

\(\textbf<40)>\) Find the equation of how much money x Joe needs to sell to earn y dollars per month.

\(\textbf<41)>\) How much does Joe need to sell to earn $10,000 in a month.

\(\textbf<42)>\) How much does Joe earn if he sells $45,000 in a month?

See Related Pages\(\)

\(\bullet\text< Word Problems- Linear Equations>\) \(\,\,\,\,\,\,\,\,\)

\(\bullet\text< Word Problems- Averages>\) \(\,\,\,\,\,\,\,\,\)

\(\bullet\text< Word Problems- Consecutive Integers>\) \(\,\,\,\,\,\,\,\,\)

\(\bullet\text< Word Problems- Distance, Rate and Time>\) \(\,\,\,\,\,\,\,\,\)

\(\bullet\text< Word Problems- Break Even>\) \(\,\,\,\,\,\,\,\,\)

\(\bullet\text< Word Problems- Ratios>\) \(\,\,\,\,\,\,\,\,\)

\(\bullet\text< Word Problems- Age>\) \(\,\,\,\,\,\,\,\,\)

\(\bullet\text< Word Problems- Mixtures and Concentration>\) \(\,\,\,\,\,\,\,\,\)

In Summary

About Andymath.com

\(\textbf\) Two car rental companies charge the following values for x miles.
Car Rental A: \(y=3x+150 \,\,\) Car Rental B: \(y=4x+100\)

\(\textbf\) Andy is going to go for a drive. The formula below tells how many gallons of gas he has in his car after m miles.
\(g=12-\frac\)

\(\bullet\text< Word Problems- Linear Equations>\)
\(\,\,\,\,\,\,\,\,\)

\(\bullet\text< Word Problems- Averages>\)
\(\,\,\,\,\,\,\,\,\)

\(\bullet\text< Word Problems- Consecutive Integers>\)
\(\,\,\,\,\,\,\,\,\)

\(\bullet\text< Word Problems- Distance, Rate and Time>\)
\(\,\,\,\,\,\,\,\,\)

\(\bullet\text< Word Problems- Break Even>\)
\(\,\,\,\,\,\,\,\,\)

\(\bullet\text< Word Problems- Ratios>\)
\(\,\,\,\,\,\,\,\,\)

\(\bullet\text< Word Problems- Age>\)
\(\,\,\,\,\,\,\,\,\)

\(\bullet\text< Word Problems- Mixtures and Concentration>\)
\(\,\,\,\,\,\,\,\,\)