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Estelle is helping at a community food drive by boxing up cans of soup. There are two sizes of boxes, large and small. Estelle fills 33 large boxes and 55 small boxes with 170170 soup cans total. The boy working next to her fills 44 large boxes and 44 small boxes with 184184 soup cans total. \newlineHow many cans does each small box hold?\newline____\_\_\_\_ cans\newline

Full solution

Q. Estelle is helping at a community food drive by boxing up cans of soup. There are two sizes of boxes, large and small. Estelle fills 33 large boxes and 55 small boxes with 170170 soup cans total. The boy working next to her fills 44 large boxes and 44 small boxes with 184184 soup cans total. \newlineHow many cans does each small box hold?\newline____\_\_\_\_ cans\newline
  1. Set up equations: Step 11: Set up the equations based on the information given.\newlineEstelle: 3L+5S=1703L + 5S = 170\newlineBoy: 4L+4S=1844L + 4S = 184\newlineHere, LL represents the number of cans in a large box, and SS represents the number of cans in a small box.
  2. Solve using elimination method: Step 22: Solve the equations using the elimination method. Multiply the first equation by 44 and the second by 33 to align the coefficients for LL. 12L+20S=68012L + 20S = 680 12L+12S=55212L + 12S = 552 Subtract the second equation from the first. 8S=1288S = 128
  3. Solve for S: Step 33: Solve for S.\newlineDivide both sides by 88.\newlineS=16S = 16\newlineThis means each small box holds 1616 cans.

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