Real-Life Word Problems: Solving Systems of Equations

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 $1,000, how many of each type of ticket were sold?

• 30 adult tickets and 120 student tickets

• 60 adult tickets and 90 student tickets

• 70 adult tickets and 80 student tickets

• 50 adult tickets and 100 student tickets

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?

• 250 miles

• 100 miles

• 200 miles

• 150 miles

A store sells two types of shirts: plain shirts for $15 each and graphic shirts for $20 each. If a customer buys a total of 8 shirts for $130, how many of each type did they buy?

• 7 plain shirts and 1 graphic shirt

• 4 plain shirts and 4 graphic shirts

• 6 plain shirts and 2 graphic shirts

• 5 plain shirts and 3 graphic shirts

A farmer has chickens and cows. If the total number of animals is 50 and the total number of legs is 140, how many chickens and how many cows does the farmer have?

• 40 chickens and 10 cows

• 25 chickens and 25 cows

• 15 chickens and 35 cows

• 30 chickens and 20 cows

A local gym offers two membership plans. Plan A costs $25 per month and Plan B costs $15 per month plus a one-time fee of $100. After how many months will the costs of both plans be the same?

• 5 months

• 12 months

• 10 months

• 8 months

A concert venue has two pricing options for tickets. Option A charges $50 per ticket, while Option B charges $30 per ticket plus a $200 flat fee for a group. How many tickets must be sold for both options to cost the same?

• 10

• 15

• 5

• 20

A delivery service charges a base fee of $10 plus $2 per mile. Another service charges a flat fee of $15 plus $1.50 per mile. How far can you travel for both services to cost the same?

• 15 miles

• 10 miles

• 20 miles

• 5 miles

A bookstore sells novels for $12 each and textbooks for $25 each. If a customer buys a total of 10 books for $180, how many novels and how many textbooks did they buy?

• 3 novels and 7 textbooks

• 6 novels and 4 textbooks

• 5 novels and 5 textbooks

• 4 novels and 6 textbooks

A bakery sells cupcakes for $3 each and cookies for $2 each. If a customer buys a total of 20 items for $50, how many cupcakes and how many cookies did they buy?

• 5 cupcakes and 15 cookies

• 15 cupcakes and 5 cookies

• 12 cupcakes and 8 cookies

• 10 cupcakes and 10 cookies

A taxi company charges a flat rate of $5 plus $2 per mile. Another company charges a flat rate of $3 plus $3 per mile. After how many miles will the costs be the same?

• 1 mile

• 4 miles

• 2 miles

• 3 miles