Substitution Challenge: Solve Real-World Systems!

1. Sarah has twice as many apples as Tom. If Tom has x apples, write an equation for the number of apples Sarah has. If together they have 30 apples, how many apples does each have?

• Tom has 10 apples and Sarah has 20 apples.

• Tom has 5 apples and Sarah has 15 apples.

• Tom has 12 apples and Sarah has 24 apples.

• Tom has 8 apples and Sarah has 16 apples.

2. 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? Set up a system of equations to solve this problem.

• 80 miles

• 100 miles

• 120 miles

• 50 miles

3. A store sells pencils for $0.50 each and erasers for $0.75 each. If a student buys a total of 10 items and spends $6.00, how many pencils and erasers did they buy?

• 5 pencils and 5 erasers

• 7 pencils and 3 erasers

• 6 pencils and 4 erasers

• 4 pencils and 6 erasers

4. The sum of two numbers is 24. One number is 4 more than the other. Write a system of equations to find the two numbers.

• The two numbers are 14 and 10.

• 20 and 4

• 16 and 8

• 12 and 12

5. A gardener is planting flowers and shrubs. If the total number of plants is 20 and the number of flowers is twice the number of shrubs, how many flowers and shrubs are there?

• 15 flowers and 5 shrubs

• 8 flowers and 12 shrubs

• 10 flowers and 10 shrubs

• 12 flowers and 6 shrubs

6. A school is selling tickets for a play. Adult tickets cost $10 and student tickets cost $5. If they sold a total of 50 tickets for $400, how many adult and student tickets were sold?

• 25 adult tickets and 25 student tickets

• 40 adult tickets and 10 student tickets

• 35 adult tickets and 15 student tickets

• 30 adult tickets and 20 student tickets

7. 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? Set up a system of equations to find the answer.

• 9 cups of sugar

• 15 cups of sugar

• 18 cups of sugar

• 12 cups of sugar

8. Two friends are saving money for a concert. One saves $5 a week and the other saves $10 a week. If they want to save a total of $100 together, how many weeks will it take for them to reach their goal?

• 7 weeks

• 12 weeks

• 10 weeks

• 5 weeks

9. A train travels 60 miles per hour and a car travels 40 miles per hour. If they start at the same time and the train is 30 miles ahead, how long will it take for the car to catch up? Set up a system of equations to solve this problem.

• 2 hours

• 1.5 hours

• 1 hour

• 3 hours

10. A bookstore sells novels for $12 each and magazines for $5 each. If a customer buys a total of 15 items and spends $100, how many novels and magazines did they buy?

• 7 novels and 8 magazines

• 2 novels and 13 magazines

• 3 novels and 12 magazines

• 5 novels and 10 magazines