Solving Equations: Isolate Variables & Check 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?

• 4 pencils and 6 erasers

• 5 pencils and 5 erasers

• 7 pencils and 3 erasers

• 6 pencils and 4 erasers

Maria has twice as many marbles as John. If John has x marbles and together they have 30 marbles, how many marbles does each person have?

• John has 5 marbles and Maria has 25 marbles.

• John has 12 marbles and Maria has 18 marbles.

• John has 10 marbles and Maria has 20 marbles.

• John has 15 marbles and Maria has 15 marbles.

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If another company charges $30 plus $0.25 per mile, how many miles must you drive for the costs to be the same?

• 500 miles

• 300 miles

• 200 miles

• 400 miles

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

• 15 girls and 20 boys

• 5 girls and 30 boys

• 10 girls and 25 boys

• 12 girls and 23 boys

A gardener is planting flowers in two different sections of a garden. The first section has 3 times as many flowers as the second section. If the total number of flowers is 48, how many flowers are in each section?

• First section: 36 flowers, Second section: 12 flowers

• First section: 40 flowers, Second section: 8 flowers

• First section: 24 flowers, Second section: 24 flowers

• First section: 30 flowers, Second section: 18 flowers

A book costs $15 and a magazine costs $5. If you buy a total of 8 items and spend $70, how many books and magazines did you buy?

• 3 books and 5 magazines

• 4 books and 4 magazines

• 2 books and 6 magazines

• 1 book and 7 magazines

A recipe requires 2 cups of flour and 3 cups of sugar. If you want to make a batch that uses 12 cups of flour, how much sugar will you need?

• 12 cups of sugar

• 10 cups of sugar

• 18 cups of sugar

• 15 cups of sugar

Two friends, Alex and Jamie, are saving money for a concert. Alex saves $5 more than twice the amount Jamie saves. If together they save $45, how much does each friend save?

• Jamie saves $10, Alex saves $35

• Jamie saves $20, Alex saves $25

• Jamie saves $13.33, Alex saves $31.66

• Jamie saves $15, Alex saves $30

A bike costs $120 and a helmet costs $30. If you buy a total of 4 items and spend $390, how many bikes and helmets did you buy?

• 1 bike and 3 helmets

• 4 bikes and 0 helmets

• 2 bikes and 2 helmets

• 3 bikes and 1 helmet

In a class, the number of girls is 4 less than three times the number of boys. If there are b boys and the total number of students is 32, how many boys and girls are there?

• 10 boys and 22 girls

• 9 boys and 23 girls

• 7 boys and 25 girls

• 8 boys and 24 girls