Systems of Equations Word Problems

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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

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

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

A sporting goods store sells left haded (x) and right handed (y) gloves. In one month, 12 gloves were sold for a total of $561. Right handed gloves cost $45 each and left handed gloves cost $52. Which system could be solved to determine the number of each type of glove sold?

• x + y = 561

  45x + 52y = 12

• x + y = 12

  52x + 45y = 561

• x + y = 12

  45x + 52y = 561

• x + y = 561

  52x + 45y = 12

Margo is taking a 160-point history test

that has a total of 50 questions. Some of the

questions are worth 6 points each, and the others

are worth 2 points each. Which system of linear

equations could be used to find, s, the correct

number of six-point questions, and t, the correct

number of two-point questions answered

correctly?

• s + 6 = 160

  6t + 2s = 50

• 6s = 2t

  s + t = 160

• 6s = 2t

  6s + 2t + 50 = 160

• s + t = 50

  6s + 2t = 160

The cafe Coffee ‘N’ Tea has a Grand Opening and sells a total of 180 items in the first two hours. They make $529 dollars. They sell coffee, C, for $2.50 per cup and tea, T, for $3.50 per cup. Which of the following systems represents their Opening Day success?

• C + T = 180

  2.5C + 3.5T = 180

• C + T = 180

  2.5C + 3.5T = 529

• C + T = 529

  2.5C + 3.5T = 529

• C - T = 180

  2.5C - 3.5T = 529

There were ​ (a)   students in each van and ​ (b)   students in each bus.

• 7

• 28

• 15

• 30

• 8

• 9

• 45

• 10

Caitlin 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 Caitlin 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

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 best represents the situation? 

• x + y = 6
  14.80x + 17y = 91

• x + y = 91
  14.80x + 17y = 6

• x + y = 6
  14.80y + 17x = 91

• x + y = 91
  14.80x+ 17y = 6