Mastering Multi-Step Equations and Variable Isolation

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?

• 4 pencils and 6 erasers

• 7 pencils and 3 erasers

• 6 pencils and 4 erasers

• 5 pencils and 5 erasers

Maria has twice as many marbles as John. If John has x marbles and together they have 36 marbles, how many marbles does each person have?

• 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 you drove x miles and your total bill was $70, how many miles did you drive?

• 80 miles

• 100 miles

• 120 miles

• 50 miles

In a class, the number of boys is 5 more than twice the number of girls. If there are g girls in the class and a total of 35 students, how many boys and girls are there?

• 12 girls and 23 boys

• 10 girls and 25 boys

• 5 girls and 30 boys

• 15 girls and 20 boys

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?

• Width: 5 meters, Length: 13 meters

• Width: 7 meters, Length: 17 meters

• Width: 6 meters, Length: 15 meters

• Width: 4 meters, Length: 10 meters

A movie theater sells adult tickets for $12 and child tickets for $8. If the total revenue from selling 50 tickets was $520, how many adult and child tickets were sold?

• 25 adult tickets and 25 child tickets

• 15 adult tickets and 35 child tickets

• 40 adult tickets and 10 child tickets

• 30 adult tickets and 20 child tickets

A recipe requires 3 cups of flour and 2 cups of sugar. If you want to make x batches of the recipe and you have 12 cups of flour and 10 cups of sugar, how many batches can you make?

• 6

• 3

• 5

• 4

A bike costs $150 and a helmet costs $30. If you have a total of $300 to spend on bikes and helmets, how many bikes and helmets can you buy?

• (3 bikes, 0 helmets)

• (1 bike, 3 helmets)

• (0 bikes, 5 helmets)

• (2 bikes, 0 helmets), (1 bike, 5 helmets), (0 bikes, 10 helmets)

In a school, the number of students in the 8th grade is 4 less than three times the number of students in the 7th grade. If there are s students in the 7th grade and a total of 80 students in both grades, how many students are in each grade?

• 7th grade: 15 students, 8th grade: 65 students

• 7th grade: 21 students, 8th grade: 59 students

• 7th grade: 25 students, 8th grade: 45 students

• 7th grade: 30 students, 8th grade: 50 students

A swimming pool can be filled by two hoses. The first hose can fill the pool in 4 hours, while the second hose can fill it in 6 hours. If both hoses are used together, how long will it take to fill the pool?

• 3 hours

• 2.4 hours

• 5 hours

• 1.5 hours