Idk L.

asked • 02/09/23

math 9th grade work

HELPP!!!!!!!!!!

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 6 cubic feet and the volume of each large box is 13 cubic feet. A total of 19 boxes of paper were shipped with a combined volume of 156 cubic feet. Determine the number of small boxes shipped and the number of large boxes shipped.

how many small boxes and large boxes where shipped


Todd G.

tutor
This problem comes down to a system of equations with two equations and two unknowns. The unknowns are the quantities of the small boxes and the large boxes. The equations are the total number of boxes(1) and the total volume shipped(2). (1) a + b = 19 (2) 6*a + 13*b = 156 where a is the number of small boxes and b is the number of large boxes. This can be solved in numerous ways but let's use the substitution method. Solving eqn 1 for a we get a = 19 - b and then plugging a into eqn 2 we have 6(19-b) + 13b = 156 Solve for b 114 - 6b + 13b = 156 combine like terms and subtract 114 from both sides 7b = 42 divide by 7 b = 6 Knowing b=6 we can now go back to eqn 1 and solve for a. a + 6 = 19 subtract 6 from both sides a = 13 Therefore the answer is 13 small boxes and 7 large boxes.
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02/09/23

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