Acontractor needs to buy nails to build a house. the nails come in small boxes and large boxes. each small box has 150 nails and each large box has 400 nails. the contractor bought 3 times as many large boxes as small boxes, which altogether had 2700 nails. determine the number of small boxes purchased and the number of large boxes purchased.

The number of small and large boxes purchased are:

Step-by-step explanation:

To solve the unknowns, two equations must be established with the information provided:

Then equation 2 is replaced in equation one and variable X is cleared:

Finally, the value of X is replaced in equation 2 to find the number of large boxes:

2 small boxes and 6 large boxes

Let x represent the number of small boxes and let y represent the number of big boxes.

Since the contractor bought 3 times as many large boxes as small boxes, hence:

y = 3x

-3x + y = 0     (1)

Also, the each small box has 150 nails and each large box has 400 nails. They were 2700 nails altogether, hence:

150x + 400y = 2700   (2)

Solve equation 1 and 2 simultaneously. First multiply equation 1 by 50 and add to (2) gives:

450y = 2700

y = 6

6 = 3x

x = 2

There were 2 small boxes and 6 large boxes purchased

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