Solving Linear Systems: Word Problems & Slope Intercepts

A bakery sells cupcakes and cookies. Each cupcake costs $2 and each cookie costs $1. If the total revenue from selling 30 items is $50, how many cupcakes and cookies were sold? Identify the slope and intercept of the revenue equation.

• 20 cupcakes and 10 cookies

• 15 cupcakes and 15 cookies

• 10 cupcakes and 20 cookies

• 25 cupcakes and 5 cookies

A school is planning a field trip. The cost per student is $15 for transportation and $10 for admission. If 40 students are going, what is the total cost? Write a system of equations to represent the situation and find the total cost.

• $600

• $500

• 1000

• $800

Two friends, Alex and Jamie, are saving money for a concert. Alex saves $5 a week, while Jamie saves $3 a week. If Alex starts with $20 and Jamie starts with $10, how many weeks will it take for them to have the same amount of money? Translate this into a system of equations.

• 5 weeks

• 3 weeks

• 7 weeks

• 10 weeks

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? Identify the slope and intercept for both companies' cost equations.

• 100 miles

• 200 miles

• 250 miles

• 150 miles

A farmer has two types of crops: corn and wheat. He can plant a maximum of 100 acres. Corn requires 2 acres per unit and wheat requires 1 acre per unit. If he wants to plant at least 40 units of crops, write a system of inequalities to represent this situation.

• 3x + y <= 100, x + y <= 30

• 2x + y <= 100, x + y >= 40

• 2x + y >= 100, x + y <= 50

• x + 2y <= 100, x + y >= 40

A concert hall has two types of tickets: regular tickets for $50 and VIP tickets for $100. If the total sales from 200 tickets is $10,000, how many of each type of ticket were sold? Set up a system of equations to solve this problem.

• 150 regular tickets and 50 VIP tickets

• 200 regular tickets and 0 VIP tickets

• 100 regular tickets and 100 VIP tickets

• 0 regular tickets and 200 VIP tickets

A gym offers two membership plans. Plan A costs $30 per month and Plan B costs $20 per month plus a one-time fee of $100. After how many months will the total cost of both plans be the same? Write a system of equations to find the answer.

• 8 months

• 5 months

• 12 months

• 10 months

A bookstore sells novels for $15 and textbooks for $25. If a customer buys a total of 10 books and spends $200, how many novels and textbooks did they buy? Create a system of equations to solve this problem.

• 4 novels and 6 textbooks

• 5 novels and 5 textbooks

• 6 novels and 4 textbooks

• 3 novels and 7 textbooks

A local theater sells adult tickets for $12 and child tickets for $8. If they sold a total of 150 tickets and made $1,440, how many adult and child tickets were sold? Formulate a system of equations to find the solution.

• 50 adult tickets and 100 child tickets

• 70 adult tickets and 80 child tickets

• 40 adult tickets and 110 child tickets

• 60 adult tickets and 90 child tickets

A delivery service charges a base fee of $10 plus $2 per mile. Another service charges a base fee of $5 plus $3 per mile. How many miles must you travel for the costs to be equal? Identify the slope and intercept for both services' cost equations.

• 10 miles

• 5 miles

• 3 miles

• 7 miles