Systems with Word Problems

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.HSA.CED.A.2

CCSS.HSA.CED.A.3

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. What would the variables represent?

• N = The cost of Nachos

  S = The cost of Steak

• N = The number of Nachos sold

  S = The number sodas sold

• 52 nachos, 35 sodas

• N = The average cost of sodas

  S = The average cost of nachos

Your family goes to a restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14.80 and some order steak for $17. If the total bill was $91, Which system of equations represent this situation?

• C + S = $17

  $91 - $17C = D

• C + S = 6

  $14.80C + $17S = $91

• C + S = 6

  $17S + $14.80C = $91

• C - S = 6

  17C - 14.80S = 91

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

• S + A = 530

  3S + 4A = 1740

• S + A = 530

  4S + 3A = 1740

• S + A = 1740

  3S + 4A = 530

• S + A = 1740

  4S + 3A = 530

Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total.

Let x = adult tickets and y = child tickets

• x + y = 21

  6x + 4y = 104

• x - y = 21

  4x + 6y = 104

• x + y = 21

  4x + 6y = 104

• 6x + 4y = 21

  x + y = 104

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

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

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

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

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50.  It turns out that the doughnuts were more popular than the coffee.  On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25.  Which equations could be used to determine the cost of the coffee? 

• 10c + 5d = 14.25
  5c + 10d = 16.50
• 10c + 5d = 16.50
  5c + 10d = 14.25
• c + d = 10
  5c + 10d = 16.50
• c + d = 5
  5c + 10d = 16.50

Tags

CCSS.8.EE.C.8C