Solving Real-World Problems with Systems of Equations

A local bakery sells cupcakes and cookies. The cost of cupcakes is $2 each and cookies are $1 each. If a customer buys a total of 10 items for $18, how many cupcakes and cookies did they buy?

• 8 cupcakes and 2 cookies

• 5 cupcakes and 5 cookies

• 7 cupcakes and 3 cookies

• 6 cupcakes and 4 cookies

Two friends, Alice and Bob, are saving money for a concert. Alice saves $5 each week, while Bob saves $3 each week. If Alice has $20 more than Bob after 4 weeks, how much money did each have initially?

• Bob had $5 more than Alice initially.

• Alice had $10 more than Bob initially.

• Alice and Bob had the same amount initially.

• Alice had $12 more than Bob initially.

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

• 200 miles

• 100 miles

• 250 miles

• 150 miles

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

• 30 adult tickets and 20 student tickets

• 20 adult tickets and 30 student tickets

• 40 adult tickets and 10 student tickets

A farmer has two types of crops: corn and wheat. He plants 3 acres of corn for every 2 acres of wheat. If he has a total of 25 acres, how many acres of each crop does he plant?

• 15 acres of corn and 10 acres of wheat

• 10 acres of corn and 15 acres of wheat

• 20 acres of corn and 5 acres of wheat

• 5 acres of corn and 20 acres of wheat

A gym charges a monthly fee of $40 plus $5 per class attended. Another gym charges a flat fee of $50 with no additional class fees. After how many classes will the costs be the same?

• 1

• 3

• 5

• 2

In a school, the ratio of boys to girls is 3:2. If there are 60 students in total, how many boys and girls are there?

• 36 boys and 24 girls

• 20 boys and 40 girls

• 40 boys and 20 girls

• 30 boys and 30 girls

A taxi company charges a base fare of $2.50 plus $0.50 per mile. Another company charges a base fare of $3.00 plus $0.40 per mile. How far do you need to travel for the fares to be equal?

• 10 miles

• 7 miles

• 5 miles

• 3 miles

A bookstore sells novels for $15 and magazines for $5. If a customer buys a total of 8 items for $70, how many novels and magazines did they buy?

• 2 novels and 6 magazines

• 4 novels and 4 magazines

• 1 novel and 7 magazines

• 3 novels and 5 magazines

Two types of tickets are sold for a concert: VIP tickets for $100 and regular tickets for $50. If 200 tickets were sold for a total of $10,000, how many of each type of ticket were sold?

• 50 VIP tickets and 150 regular tickets

• 100 VIP tickets and 100 regular tickets

• 200 VIP tickets and 0 regular tickets

• 0 VIP tickets and 200 regular tickets