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 all together had 2500 nails. Determine the number of small boxes purchased and the number of large boxes purchased. PLEASE HELP!!

Answer 1

The contractor bought 4 large boxes and 7 small boxes of nails, with the large boxes containing 450 nails each, and the small boxes containing 100 nails each to reach a total of 2500 nails.

Step-by-step explanation:

The contractor is faced with a classic algebra problem. To solve it, let's denote the number of large boxes as x and thus the number of small boxes as x + 3, because he bought 3 more small boxes than large ones. According to the problem, each small box contains 100 nails, and each large box contains 450 nails. With the total number of nails being 2500, we can write the equation:

100(x + 3) + 450x = 2500

Solving for x gives us the number of large boxes, and adding 3 to that number gives us the number of small boxes. Let's solve the equation:

100x + 300 + 450x = 2500

550x + 300 = 2500

550x = 2500 - 300

550x = 2200

x = 2200 / 550

x = 4

Therefore, the contractor bought 4 large boxes and 4 + 3 = 7 small boxes.

Answer 2

Answer: Let's call the number of large boxes purchased "L" and the number of small boxes purchased "S".

From the problem, we know that:

Each small box has 100 nails, so the total number of nails from the small boxes is 100S.

Each large box has 450 nails, so the total number of nails from the large boxes is 450L.

The contractor bought 3 more small boxes than large boxes, so S = L + 3.

The total number of nails purchased is 2500, so 100S + 450L = 2500.

We can use the second equation to solve for one of the variables in terms of the other. For example, we can solve for L:

100S + 450L = 2500

Substituting S = L + 3:

100(L + 3) + 450L = 2500

Expanding the parentheses:

100L + 300 + 450L = 2500

Combining like terms:

550L + 300 = 2500

Subtracting 300 from both sides:

550L = 2200

Dividing both sides by 550:

L = 4

So the contractor purchased 4 large boxes of nails.

We can use the equation S = L + 3 to find the number of small boxes purchased:

S = L + 3 = 4 + 3 = 7

So the contractor purchased 7 small boxes of nails.

Therefore, the contractor purchased 4 large boxes and 7 small boxes of nails.

Step-by-step explanation: