Linear Equations Word Problems

Write a linear equation. Do NOT solve. Use "C" and "m" for your variables.

The local service center advertises that it charges a flat fee of $50 plus $8 per mile to tow a vehicle. Write an equation that represents the total cost (C) of a service for m miles of towing.

• C = 50 + 8m
• C = 50 + 5m
• C = 50 - 8m
• C = 8m - 50

Write a linear equation. Do NOT solve. Use "x" and "y" for your variables.

Kate bought $23.40 worth of two types of bird seed. Thistle bird seed sells for $1.60 per pound and Wild bird seed sells for $0.95 per pound. Write an equation to find the total amount of pounds of bird seed purchased.

• 1.60x + 0.95y = 23.40
• 1.60x + 0.95y = 20.00
• 2.00x + 0.80y = 23.40
• 1.50x + 1.00y = 23.40

Write a system of linear equations. Do NOT solve. Use "a" and "c" for your variables.

A school is selling tickets for a fundraiser. On the first day, they sold 12 adult tickets and 8 child tickets for $200. On the second day, they sold 10 adult tickets and 15 child tickets for $250. What is the cost of an adult ticket and a child ticket?

• 12a + 10c = 200, 8a + 15c = 250
• 10a + 8c = 200, 12a + 15c = 250
• 12a + 8c = 250, 10a + 15c = 200
• 12a + 8c = 200, 10a + 15c = 250

Write linear equations. Do NOT solve. Use "a" and "c" as your variables.

A group of friends buys 5 adult tickets and 3 child tickets for a movie and spends $62. Another group buys 2 adult tickets and 6 child tickets for $46. What is the price of an adult ticket and a child ticket?

• 5a + 5c = 80; 3a + 2c = 40
• 4a + 2c = 50; 3a + 4c = 70
• 6a + 1c = 64; 1a + 5c = 30
• 5a + 3c = 62; 2a + 6c = 46

Write a system of linear equations. Do NOT solve. Use "b" and "r" as your variables.

A rental shop charges $12 per hour for mountain bikes and $8 per hour for road bikes. If a group rents 3 mountain bikes and 4 road bikes for $76, and another group rents 5 mountain bikes and 2 road bikes for $88, how much does it cost to rent each type of bike per hour?

• 3b + 4r = 76; 5b + 2r = 88
• 4b + 3r = 76; 3b + 5r = 88
• 2b + 4r = 76; 6b + 2r = 88
• 3b + 2r = 76; 5b + 4r = 88

Write a system of linear equations. Do NOT solve. Use "a" and "b" as your variables.

At a fruit stand, 3 apples and 4 bananas cost $12.50, and 5 apples and 2 bananas cost $15.50. What is the price of one apple and one banana?

• 3a + 4b = 12.50, 5a + 2b = 15.50
• 2a + 3b = 10.00, 4a + 5b = 20.00
• 3a + 2b = 10.00, 6a + 4b = 18.00
• 1a + 1b = 5.00, 2a + 3b = 8.00

Write a system of equations. Do NOT solve. Use "v" and "r" as your variables.

A music band sells tickets for a concert. VIP tickets cost $50, and regular tickets cost $30. If the band sells 80 tickets and makes $3,100, how many of each type of ticket were sold?

• v + r = 80; 50v + 30r = 3100
• v + r = 90; 50v + 30r = 3200
• v + r = 60; 50v + 30r = 2800
• v + r = 100; 50v + 30r = 2500

Write a system of linear equations. Do NOT solve. Use "n" and "m" as your variables.

In a bookstore, 2 novels and 3 magazines cost $28, while 4 novels and 2 magazines cost $40. How much does each novel and magazine cost?

• 2n + 2m= 28;

  4n + 3m=40

• 4n + 2m=40;

  2n + 4m=28

• 2n + 3m=28;

  4n + 2m=40

• 4n + 3m=28;

  2n + 4m=40

Write a system of linear equations. Do NOT solve. Use "i" and "f" as your variables.

A swimming pool sells season passes for individuals and families. Individual passes cost $50, and family passes cost $120. If the pool sells 30 passes and collects $3,300, how many individual and family passes were sold?

• i + f=3300;

  50i + 120f=30

• i + f=30;

  50i + 120f=3300

• 50i + f=30;

  i + 120f=3300

• i + f=30;

  120i + 50f=3300

Write a system of equations. Do NOT solve. Use "k" and "p" for the variables.

A landscaper plants oak and pine trees. Each oak tree takes 1 hour to plant, and each pine tree takes 1.5 hours. If the landscaper plants 8 trees in 10 hours, how many of each type of tree were planted?

• k + p = 8;

  k + 1.5p = 10

• k + 2p = 10;

  k + p = 8

• k + p = 10;

  k + 1.5p = 8

• k + p = 10;

  k + 2p = 8