Substitution Method Word Problems

Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin? Choose the system that matches the situation.

• e + a = 33

  a = 2e - 3

• e + a = 33

  e = 2a - 3

• e+ a = 33

  e = 3 - 2a

• e + a = 3

  e = 33 - 2a

At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, t, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?

• t + n = 54
  t = 3n + 8

• t + n = 54
  n = 3t + 8

• t + n = 54
  t = 3n - 8

• t + n = 8
  t = 3n + 54

Last season two running backs on the Steelers football team rushed a combined total of 1550 yards. One rushed 4 times as many yards as the other. Let x and y represent the number of yards each individual player rushed. Which system of equations could be used?

• x + y = 1550
  y  = 4x

• x + y = 1550
  y = x + 4

• y - x = 1550
  y = 4x

• y = 1550 + x
  y = x + 4

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used?

• 1s + 3c = 38
  2s + 3c = 52

• 3s + 1c = 38
  3s + 2c = 52

• s + c = 38
  s + c = 52

• 3s + 3c = 38
  1s + 2c = 52

The sum of Mr. Micklow and Ms. Craft's age is 55.  The difference is 3.  
Solve:
x + y = 55
x - y = 3

• (26, 23)

• (26, 29)

• (29, 26)

• (29, 32)

Amy sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Adam sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60. What is the price of 1 pack of sugar cookies and 1 pack of oatmeal cookies?

• Sugar Cookies $5 
  Oatmeal Cookies $3

• Sugar Cookies $4
  Oatmeal Cookies $8

• Sugar Cookies $2
  Oatmeal Cookies $6

• Sugar Cookies $3
  Oatmeal Cookies $6

Define the variables for this systems word problem. (Defina las variables para este problema de palabras del sistema.)

• x - # of multiple choice questions & y - # of word problems//x - # de preguntas de elección múltiple e y - # de problemas de palabras

• x - 1 point and y - 5 points//x - 1 puntos e y - 5 puntos

• x - 40 questions & y - 100 points//x - 40 preguntas e y - 100 puntos

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

Gabby and Sydney bought some pens and pencils. Gabby bought 4 pens and 5 pencils for $6.71. Sydney bought 5 pens and 3 pencils for $7.12. Find the cost of each.

• The cost of a pen is $1.19 and the cost of a pencil is $0.39.

• The cost of a pencil is $1.19 and the cost of a pen is $0.39.

• The cost of a pen is $6.71 and the cost of a pencil is $7.12.

• The cost of a pen is $7.12 and the cost of a pencil is $6.71.

The first step in solving using the substitution method is __________.

• get x by itself

• get y by itself

• get either variable by itself in one equation

• add the equations together