Question

a contractor needs to buy nails to build a house. the nails come in small boxes and large boxes. each small box has 100 nails and each large box has 450 nails. the contractor bought 3 more small boxes than large boxes, which altogether had 2500 nails. determine the number of small boxes purchased and the number of large boxes purchased.

answer attempt 1 out of 2

there were \boxed{} small boxes purchased and \boxed{} large boxes purchased.

Explanation:

Step1: Define Variables

Let \( x \) be the number of large boxes. Then the number of small boxes is \( x + 3 \).

Step2: Set Up Equation

Each small box has 100 nails, so small boxes contribute \( 100(x + 3) \) nails. Each large box has 450 nails, so large boxes contribute \( 450x \) nails. Total nails are 2500, so:

$$ 100(x + 3) + 450x = 2500 $$

Step3: Solve the Equation

Expand: \( 100x + 300 + 450x = 2500 \)
Combine like terms: \( 550x + 300 = 2500 \)
Subtract 300: \( 550x = 2200 \)
Divide by 550: \( x = 4 \)

Step4: Find Number of Boxes

Large boxes: \( x = 4 \)
Small boxes: \( x + 3 = 4 + 3 = 7 \)

Answer:

There were 7 small boxes purchased and 4 large boxes purchased.