Solving Real-World Problems with Systems of Equations

1. Sarah has twice as much money as Tom. Together, they have $60. How much money does each person have? Identify the variables and interpret the solution in context.

• Tom has $30 and Sarah has $30.

• Tom has $25 and Sarah has $35.

• Tom has $10 and Sarah has $50.

• Tom has $20 and Sarah has $40.

2. A store sells pencils for $0.50 each and erasers for $0.75 each. If a student buys a total of 10 items for $6.00, how many pencils and erasers did they buy? Define the variables and explain the solution.

• 5 pencils and 5 erasers

• 6 pencils and 4 erasers

• 7 pencils and 3 erasers

• 4 pencils and 6 erasers

3. Emily and Jake are saving money for a concert. Emily saves $5 each week, while Jake saves $3 each week. If they want to save a total of $50 together, how many weeks will it take? Identify the constants and interpret the result.

• 8 weeks

• 10 weeks

• 7 weeks

• 5 weeks

4. A movie theater sells adult tickets for $12 and child tickets for $8. If 50 tickets were sold for a total of $480, how many adult and child tickets were sold? Define the variables and explain the solution in context.

• 10 adult tickets and 40 child tickets were sold.

• 25 adult tickets and 25 child tickets were sold.

• 20 adult tickets and 30 child tickets were sold.

• 15 adult tickets and 35 child tickets were sold.

5. Lisa and Mark are selling cookies and brownies. Each cookie sells for $2 and each brownie for $3. If they sold a total of 30 items for $60, how many of each did they sell? Identify the variables and interpret the solution.

• 15 cookies and 15 brownies

• 10 cookies and 20 brownies

• 5 cookies and 25 brownies

• 0 cookies and 30 brownies

6. A farmer sells apples for $1.20 per pound and oranges for $0.80 per pound. If he sold a total of 50 pounds of fruit for $48, how many pounds of each fruit did he sell? Define the constants and explain the solution.

• 20 pounds of apples and 30 pounds of oranges

• 25 pounds of apples and 25 pounds of oranges

• 10 pounds of apples and 40 pounds of oranges

• 15 pounds of apples and 35 pounds of oranges

7. Two friends, Alex and Jamie, are collecting coins. Alex has 3 times as many quarters as Jamie. If together they have 40 quarters, how many quarters does each have? Identify the variables and interpret the solution in context.

• Jamie has 20 quarters and Alex has 20 quarters.

• Jamie has 5 quarters and Alex has 35 quarters.

• Jamie has 10 quarters and Alex has 30 quarters.

• Jamie has 15 quarters and Alex has 25 quarters.

8. A bookstore sells novels for $10 and magazines for $5. If a customer buys a total of 15 items for $100, how many novels and magazines did they buy? Define the variables and explain the solution.

• 5 novels and 10 magazines

• 7 novels and 8 magazines

• 3 novels and 12 magazines

• 10 novels and 5 magazines

9. A car rental company charges a flat fee of $30 plus $0.20 per mile driven. If a customer paid $50 for a rental, how many miles did they drive? Identify the constants and interpret the solution in context.

• 50 miles

• 100 miles

• 120 miles

• 80 miles

10. A charity event sells tickets for $15 each and donations of $5 each. If they raised a total of $300 from 20 tickets and donations, how many tickets and donations were made? Define the variables and explain the solution.

• 5 tickets and 15 donations

• 20 tickets and 0 donations

• 10 tickets and 10 donations

• 15 tickets and 5 donations