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A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. The volume of each small box is 10 cubic feet and the volume of each large box is 18 cubic feet. There were twice as many small boxes shipped as large boxes shipped and the total volume of all boxes was 190 cubic feet. Write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. Define the variables that you use to write the system.

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The Number of small and large boxes shipped are 10 and 5 respectively.

Large boxes :

  • Volume = 18 cubic feets
  • Let number of large boxes = b

Small boxes :

  • Volume = 10 cubic feets
  • Number of small boxes = 2b

Total volume shipped = 190 cubic feet

To obtain total volume shipped :

(Number of small boxes × volume of small boxes) + (Number of large boxes × volume of large boxes

Writing as a system of equation :

  • (10 × 2b) + (18 × b)
  • 20b + 18b = 190 cubic feets
  • 38b = 190
  • b = 190 ÷ 38
  • b = 5

Hence,

  • Number of large boxes = 5
  • Number of small boxes = 2(5) = 10

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