Real-Life Equation Problems: Check & Interpret 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.

• 5 pencils and 5 erasers

• 6 pencils and 4 erasers

• 7 pencils and 3 erasers

• 4 pencils and 6 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? Interpret the results in terms of their collection sizes.

• John has 18 marbles, Maria has 18 marbles.

• John has 10 marbles, Maria has 26 marbles.

• John has 12 marbles, Maria has 24 marbles.

• John has 15 marbles, Maria has 21 marbles.

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Another company charges $30 plus $0.25 per mile. How many miles would you need to drive for both companies to charge the same amount? Check your solution by calculating the total cost for both companies.

• 300 miles

• 500 miles

• 200 miles

• 400 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? Interpret the results in terms of the gender ratio.

• 20 boys and 15 girls

• 30 boys and 5 girls

• 15 boys and 20 girls

• 25 boys and 10 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? Check your solution by calculating the perimeter with your found dimensions.

• Width: 7 meters, Length: 15 meters

• Width: 5 meters, Length: 13 meters

• Width: 4 meters, Length: 10 meters

• Width: 6 meters, Length: 12 meters

Two friends, Alex and Jamie, are saving money for a concert. Alex has $20 more than Jamie. If together they have $140, how much does each friend have? Interpret the results in terms of their savings goals.

• Jamie has $30 and Alex has $50.

• Jamie has $50 and Alex has $70.

• Jamie has $60 and Alex has $80.

• Jamie has $40 and Alex has $60.

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? Check your solution by maintaining the ratio of flour to sugar.

• 2 cups of sugar

• 4 cups of sugar

• 3.33 cups of sugar

• 1.5 cups of sugar

A bike costs $150, and a helmet costs $30. If you have a total budget of $240, how many bikes and helmets can you buy? Interpret the results in terms of your budget constraints.

• 0 bikes and 10 helmets

• 1 bike and 5 helmets

• You can buy 1 bike and 3 helmets, or 0 bikes and 8 helmets.

• 2 bikes and 1 helmet

In a class, the number of girls is 4 less than three times the number of boys. If there are 32 students in total, how many boys and girls are in the class? Check your solution by adding the number of boys and girls together.

• 9 boys and 27 girls

• 10 boys and 22 girls

• 8 boys and 24 girls

• 7 boys and 25 girls

A bookstore sells novels for $12 each and magazines for $5 each. If you buy a total of 8 items and spend $66, how many novels and magazines did you buy? Interpret the results in terms of your reading preferences.

• 4 novels and 4 magazines

• 3 novels and 5 magazines

• 2 novels and 6 magazines

• 5 novels and 3 magazines