Question

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.

Answer 1

Answer:

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:

1. 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)
2. 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

Answer 2

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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