Real-World Linear Equations: Check Your Solutions!

A store sells pencils for $2 each and erasers for $3 each. If you buy a total of 10 items and spend $24, how many pencils and erasers did you buy? Check your solution by substituting back into the equations.

• 7 pencils and 3 erasers

• 6 pencils and 4 erasers

• 4 pencils and 6 erasers

• 5 pencils and 5 erasers

Maria has twice as many marbles as John. If the total number of marbles they have is 36, how many marbles does each person have? Verify your answer by adding the number of marbles together.

• John has 10 marbles and Maria has 26 marbles.

• John has 15 marbles and Maria has 21 marbles.

• John has 12 marbles and Maria has 24 marbles.

• John has 18 marbles and Maria has 18 marbles.

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If a customer pays $70, how many miles did they drive? Confirm your solution by calculating the total cost based on the miles driven.

• 100 miles

• 150 miles

• 50 miles

• 200 miles

In a school, the number of boys is 5 more than twice the number of girls. If there are 35 students in total, how many boys and girls are there? Check your solution by adding the number of boys and girls together.

• 15 boys and 20 girls

• 30 boys and 5 girls

• 25 boys and 10 girls

• 20 boys and 15 girls

A gardener has a rectangular garden where the length is 3 meters more than twice the width. If the perimeter of the garden is 36 meters, what are the dimensions of the garden? Verify your answer by calculating the perimeter with the found dimensions.

• Width: 4 meters, Length: 10 meters

• Width: 5 meters, Length: 13 meters

• Width: 6 meters, Length: 12 meters

• Width: 7 meters, Length: 15 meters

Two friends, Alex and Jamie, are saving money for a concert. Alex has $20 more than Jamie, and together they have $120. How much does each friend have? Check your solution by adding their amounts together.

• Jamie has $30, Alex has $50.

• Jamie has $40, Alex has $60.

• Jamie has $50, Alex has $70.

• Jamie has $60, Alex has $80.

A recipe requires 3 cups of flour and 2 cups of sugar. If you want to make a batch that uses 5 cups of flour, how much sugar will you need? Verify your answer by setting up a proportion based on the original recipe.

• 1.5 cups of sugar

• 3.33 cups of sugar

• 4 cups of sugar

• 2 cups of sugar

A bike costs $150, and a helmet costs $30. If you buy a total of 5 items for $600, how many bikes and helmets did you buy? Check your solution by substituting back into the equations.

• 3 bikes and 2 helmets

• 1 bike and 4 helmets

• 2 bikes and 3 helmets

• 4 bikes and 1 helmet

In a class, the number of girls is 4 less than three times the number of boys. If there are 28 students in total, how many boys and girls are there? Verify your answer by adding the number of boys and girls together.

• 6 boys and 22 girls

• 10 boys and 18 girls

• 12 boys and 16 girls

• 8 boys and 20 girls

A phone plan costs $30 per month plus $0.10 per text message. If a customer pays $50 this month, how many text messages did they send? Confirm your solution by calculating the total cost based on the number of messages sent.

• 100

• 150

• 250

• 200