Question

A contractor needs to buy nails to build a house. The nails come in small boxes and large boxes. Each small box has 200 nails and each large box has 400 nails. The contractor bought twice as many small boxes as large boxes, which altogether had 3200 nails. Graphically solve a system of equations in order to determine the number of small boxes purchased, x,x, and the number of large boxes purchased, yy.

Answer 1

Answer: 21

Explanation:

Answer 2

Based on the graph, a solution for the system of equations is (8, 4).

The number of small boxes purchased is 8 small boxes.

The number of large boxes purchased is 4 large boxes.

In order to write a system of linear equations to describe this situation, we would assign variables to the number of boxes purchased, and then translate the word problem into algebraic equation as follows:

• Let the variable x represent the number of small boxes purchased.
• Let the variable y represent the number of large boxes purchased.

Since each small box contains 200 nails and each large box has 400 nails, with a total of 3200 nails;

200x + 400y = 3200. ..........equation 1.

Additionally, the contractor bought twice as many small boxes as large boxes;

x = 2y ..........equation 2.

Next, we would use an online graphing calculator to graphically solve the system of linear equations. Therefore, the required solution for the given system of linear equations is the point of intersection of the two lines on the graph, which is given by the ordered pair (8, 4)