Solving Systems of Equations in Real-Life Scenarios

1. A school is selling tickets for a play. Adult tickets cost $10 each and student tickets cost $5 each. If the school sold a total of 150 tickets for $1,200, how many adult and student tickets were sold?

• 100 adult tickets and 50 student tickets

• 80 adult tickets and 70 student tickets

• 60 adult tickets and 90 student tickets

• 90 adult tickets and 60 student tickets

2. Two friends, Alex and Jamie, are saving money for a concert. Alex saves $15 each week, while Jamie saves $10 each week. If Alex has already saved $30 and Jamie has saved $20, how many weeks will it take for them to have the same amount saved?

• 1 week

• 4 weeks

• 2 weeks

• 3 weeks

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

• 300 miles

• 200 miles

• 500 miles

• 400 miles

4. A farmer has chickens and cows. If the total number of animals is 50 and there are 150 legs in total, how many chickens and cows does the farmer have?

• 10 chickens and 40 cows

• 25 chickens and 25 cows

• 20 chickens and 30 cows

• 30 chickens and 20 cows

5. A local gym offers two membership plans. Plan A costs $30 per month, and Plan B costs $20 per month plus a one-time fee of $60. After how many months will the cost of both plans be the same?

• 6 months

• 10 months

• 8 months

• 4 months

6. A store sells pencils for $0.50 each and erasers for $1.00 each. If a student buys a total of 20 items and spends $12, how many pencils and erasers did the student buy?

• 18 pencils and 2 erasers

• 10 pencils and 10 erasers

• 16 pencils and 4 erasers

• 12 pencils and 8 erasers

7. A taxi company charges a base fare of $3 plus $2 per mile. Another taxi company charges a base fare of $5 plus $1.50 per mile. How far do you need to travel for the fares to be equal?

• 5 miles

• 2 miles

• 3 miles

• 4 miles

8. In a class, the ratio of boys to girls is 3:2. If there are 30 students in total, how many boys and girls are there?

• 15 boys and 15 girls

• 20 boys and 10 girls

• 10 boys and 20 girls

• 18 boys and 12 girls

9. A bookstore sells novels for $12 each and magazines for $5 each. If a customer buys a total of 10 items and spends $80, how many novels and magazines did they buy?

• 2 novels and 8 magazines

• 5 novels and 5 magazines

• 3 novels and 7 magazines

• 4 novels and 6 magazines

10. A delivery service charges a flat fee of $10 plus $1.50 per mile. Another service charges a flat fee of $5 plus $2 per mile. How many miles must you travel for the costs to be the same?

• 10 miles

• 15 miles

• 5 miles

• 20 miles