Solving Real-Life Systems of Equations for 8th Graders

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. Another company charges $20 plus $0.25 per mile. How many miles must you drive for both companies to charge the same amount?

• 150 miles

• 200 miles

• 100 miles

• 250 miles

A local gym charges a monthly fee of $40 plus $5 for each class attended. Another gym charges a $30 monthly fee plus $8 per class. How many classes must you attend for both gyms to cost the same?

• 2

• 6

• 10

• 4

A school is selling tickets for a play. Adult tickets cost $10 each, and student tickets cost $5 each. If the total revenue from ticket sales is $200, how many adult and student tickets were sold if the number of adult tickets sold is twice the number of student tickets?

• 16 adult tickets and 8 student tickets

• 10 adult tickets and 5 student tickets

• 20 adult tickets and 5 student tickets

• 12 adult tickets and 6 student tickets

Two friends are saving money to buy a video game. Friend A saves $15 a week, while Friend B saves $10 a week but has $20 already saved. How many weeks will it take for both friends to have the same amount saved?

• 3 weeks

• 4 weeks

• 5 weeks

• 6 weeks

A bakery sells cupcakes for $3 each and cookies for $2 each. If a customer buys a total of 20 items and spends $54, how many cupcakes and cookies did they buy?

• 12 cupcakes and 8 cookies

• 16 cupcakes and 4 cookies

• 10 cupcakes and 10 cookies

• 14 cupcakes and 6 cookies

A phone company offers two plans. Plan A costs $50 per month with unlimited data, while Plan B costs $30 per month plus $10 for each GB of data used. For what amount of data usage will both plans cost the same?

• 3 GB

• 1 GB

• 2 GB

• 5 GB

A farmer has two types of fruit trees. Apple trees produce 100 apples each and peach trees produce 150 peaches each. If the farmer has a total of 600 apples and peaches, and the number of apple trees is twice the number of peach trees, how many of each type of tree does the farmer have?

• 30 apple trees and 5 peach trees

• 10 apple trees and 20 peach trees

• 24 apple trees and 12 peach trees

• 20 apple trees and 15 peach trees

A concert venue has two pricing options for tickets. Option A charges $25 per ticket, while Option B charges $15 per ticket plus a $10 service fee. How many tickets must be sold for both options to generate the same revenue?

• 2

• 3

• 5

• 1

A bookstore sells novels for $12 each and magazines for $5 each. If a customer buys a total of 15 items and spends $120, how many novels and magazines did they buy?

• 7 novels and 8 magazines

• 6 novels and 9 magazines

• 5 novels and 10 magazines

• 4 novels and 11 magazines

A delivery service charges a base fee of $10 plus $2 per mile. Another service charges $5 plus $3 per mile. How many miles must be traveled for both services to cost the same?

• 7 miles

• 5 miles

• 3 miles

• 10 miles