A contractor 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.

Question

Clarence

Mathematics

26 September, 00:22

A contractor 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.

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Answers (1)

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Sam Morse · Answer 1

The number of small and large boxes purchased are:

2 small boxes. 6 large boxes.

Step-by-step explanation:

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

150X + 400Y = 2700 (the price of the boxes and the final number of nails, where X is the small boxes and Y the large boxes) Y = 3X (Large boxes are triple the small ones)

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

150X + 400 (3X) = 2700 150X + 1200X = 2700 1350X = 2700 X = 2700/1350 X = 2

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

Y = 3X Y = 3 (2) Y = 6