Setting Up Systems Word Problems

The difference between two numbers is 35. One-half the larger number plus one-third the smaller is 30. Find the numbers.

Tags

CCSS.8.EE.C.8C

Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of $203. Ming sold 11 small boxes and 11 large boxes of oranges for a total of $220. Find the cost of one small box of oranges and one large box of oranges. (x = small and y = large)

• 3x + 11y = 203

  14x + 4y = 220

• 3x + 14y = 220

  11x + 11y = 203

• 3x + 14y = 203

  11x + 11y = 220

• 3x - 14y = 203

  11x - 11y = 220

Tags

CCSS.8.EE.C.8C

A group of freshman went on the water drip field trip. During the field trip a total of 180 ticks and mosquitoes were slapped. If these pests had a total of 1240 legs, how many mosquitoes and how many ticks were slapped during the field trip? (Hint: Ticks have 8 legs and mosquitoes have 6 legs.) and use x = ticks and y = mosquitoes

• x + y = 180

  8x + 6y = 1240

• x + y = 1240

  8x + 6y = 180

• x + 6y = 180

  8x + y = 1240

• x + y = 180

  6x + 8y = 1240

Tags

CCSS.8.EE.C.8C

The sum of two numbers is 23.6. One is four times the other. Find the number.

• x + y = 23.6

  x = 4y 

• x - y = 23.6

  x = 4y 

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

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

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

Josh is thinking of two numbers. Their sum is -10 and their difference is -2. Which system of equations represents the situation?

• x - y = -10
  x + y = -2

• x = -2
  y = 5

• x + y = -2
  x - y = -10

• x + y = -10
  x - y = -2

Tags

CCSS.HSA.CED.A.3

Yazzy won a bag full of money! She has 49 bills in all. She counts $1430. There are twenty dollar bills and fifty dollar bills. How many of each bill does Yazzy have?  Which system best represents the situation? 

• x + y = 1430
  20x + 50y = 49

• x + y = 49
  10x + 5y = 1430 

• x + y = 49
  20x + 50y = 1430

• x + y = 49
  x + y = 1430

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