Systems With Substitution Word Problems

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

Tags

CCSS.HSA.CED.A.3

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

Tags

CCSS.8.EE.C.8C

Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all.  Upon completing the job he counted out the coins and it came to $6.60.  Which system of equations could be used to find the exact number of dimes and nickels? 

• d + n = 6.60
  .10d + .05n = 80

• d + n = 80
  d + n = 6.60

• d + n = 80
  .10d + .05n = 6.60

• d + n = 80
  .05d + .10n = 6.60

Tags

CCSS.8.EE.C.8C

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

Tags

CCSS.8.EE.C.8C

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

Tags

CCSS.8.EE.C.8C

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

Tags

CCSS.HSA.CED.A.3

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

Tags

CCSS.8.EE.C.8C

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)

Tags

CCSS.8.EE.C.8C

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

• 4y = 3x + 64

  8y = x + 68

• 4y = 3x + 64

  8y = x + 60

• 3x + 4y = 64

  x + 8y = 68

• 3x + 4y = 64

  x + 8y = 60

Tags

CCSS.8.EE.C.8C

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes.  Which system of equations represents the situation?

• 3x + 2y = 315
  2x + 4y = 450

• 3x + 2y = 450
  2x + 4y = 315

• 2x + 2y = 315
  3x + 4y = 450

Tags

CCSS.HSA.CED.A.3