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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. Each small box of paper weighs 45 pounds and each large box of paper weighs 70 pounds. There were 6 more small boxes shipped than large boxes and the total weight of all boxes was 1305 pounds. Determine the number of small boxes shipped and the number of large boxes shipped.

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MathPhys

Step-by-step explanation:

Let's say S is the number of small boxes and L is the number of large boxes.

There were 6 more small boxes than large boxes, so:

S = L + 6

Each small box weighs 45 pounds, and each large box weighs 70 pounds.  The total weight was 1305 pounds, so:

45S + 70L = 1305

We can now solve the system of equations.  Using substitution:

45(L + 6) + 70L = 1305

45L + 270 + 70L = 1305

115L = 1035

L = 9

S = 9 + 6

S = 15

There are 15 small boxes and 9 large boxes.

adioabiola

We are required to determine the number of small boxes shipped and the number of large boxes shipped.

let

x = number of small boxes shipped

y = number of large boxes shipped

Weight of small boxes = 45 pounds

Weight of large boxes = 70 pounds

Total weight of boxes = 1305 pounds

There were 6 more small boxes shipped than large boxes

x = y + 6 (1)

x = y + 6 (1)45x + 70y = 1305 (2)

substitute x = y + 6 into (2)

45x + 70y = 1305

45(y + 6) + 70y = 1305

45y + 270 + 70y = 1305

45y + 70y = 1305 - 270

115y = 1035

divide both sides by 115

y = 1035 / 115

y = 9

Recall,

x = y + 6

x = 9 + 6

x = 15

Therefore,

the number of small boxes shipped is 15 and the number of large boxes shipped is 9

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