System of Equations (Substitution) Word Problem

Sam has been planting young trees in his garden. The maple tree that is 30 inches tall is growing 3 inches per month, whereas the oak tree that is 35 inches tall is growing 2 inches per month. Write and solve the system. Let x represent the number of months and let y represent the total height of the tree. How many months will it take for both trees to be the same height? What height will they both be?

• 5 months for a height of 45 inches

• 2 months for a height of 36 inches

• 7 months for a height of 49 inches

• 3 months for a height of 39 inches

A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. Which system of equations could be used to find the number of toppings when both companies cost the same amount?

• y = 6.80 + .65x
  y=7.30+.90x

• x + y = 6.80
  x + y = 7.30

• y = 6.80+.90x
  y = 7.30 + .65x

• y + .90x = 6.80
  y + .65x = 7.30

At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. If a system of equations is written, which would be the correct representation of the 2 variables?

• t: # of tacos
  m: # of glasses of milk

• t: Cost of each taco
  m: Cost of each glass of milk

• t: total cost
  m: # of food items

• t: Cost of each glass of milk
  m: Cost of each taco

Jacob bought a total of 9 pizzas for his class party. The amount of large pizzas was twice the amount of medium pizzas. How many large and how many medium pizzas did he buy? Which of the two equations below represent this situation. Select two answers.

• x + y = 9

• x = 2y

• y = 2x

• xy = 9

Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. Which equation represents the number of shirts when both companies charge the same amount? Let x represent the number of shirts and y represent the total cost. Hint one equation is in blue and the other is in green.

• y = 9.65 + x

  y = 8.40 + x

• y = 9.65x + 43

  y = 8.40x + 58

• y =9.65x

  y = 8.40x

• y = 9.65x - 43

  y = 8.40x - 58

Mika and her friend Cindy are knitting scarves for the homeless. Mika had already completed 10 scarves and has committed to making 6 more scarves per day. Cindy, who has not completed any scarves yet, has more free time and can make 8 scarves per day. Write and solve the system. Let x represent the number of days and let y represent the total number of scarves. How long will that take for Mika and Cindy to have made the same amount of scarves? How many scarves will both of them have made?

• 2 days to have 16 scarves

• 5 days to have 40 scarves

• 3 days to have 28 scarves

• 7 days to have 56 scarves

Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. Which equation represents the number of shirts when both companies charge the same amount?

• y = 9.65 + x
  y = 8.40 + x

• y = 9.65x + 43
  y = 8.40x + 58

• y =9.65x
  y = 8.40x

• y = 9.65x - 43
  y = 8.40x - 58

One number is eight less than four times the other number. The sum of the two numbers is 37. Find the numbers. Write a system of equations to represent this situation.

• x = 8 - 4y

  x + y = 37

• x = 4y - 8

  x+ y = 37

• x - 8 = 4y

  x + y = 37

• x - 8y = 4

  x + y = 37

Mrs. Travis wants to have a clown deliver balloons to her secretary’s office. Clowns R Fun charges $1.50 per balloon and $4 delivery. Singing Balloons charges $2 per balloon and $2 for delivery. What are the two equations?

• y=4x + 1.50

  y=2x+2

• y=2x + 4

  y = 1.50x + 2

• y = 1.50x + 4

  y = 2x + 2

• 1.50x + 4y = 2

  x + y = 2

Which system of equations could represent the following word problem? The sum of two numbers is 30. The first number is twice the second minus 5.

• a + b = 30

  2a = b - 5

• a - b = 30

  2a = b - 5

• a + b = 5

  a = 2b -30

• a + b = 30

  a = 2b - 5