Question

Mr. Nall purchased a total of 26 pieces of lumber to build a small deck. The longer 1x6 boards cost $5.97 each and the shorter 2x6 boards cost $4.97 each. If he spent a total of $149.22 excluding tax, how many of each type did he buy?

Answer 1

Mr. Nall bought 21 units of 1x6 boards for $5.97 each and 5 units of 2x6 boards for $4.97 each, making up the total purchase of $149.22 for 26 pieces of lumber.

Step-by-step explanation:

To find out how many of each type of lumber Mr. Nall bought, we need to set up a system of equations based on the information provided. Let's denote the number of 1x6 boards as x and the number of 2x6 boards as y.

From the problem, we have two equations:

1. The total number of boards purchased is 26: x + y = 26
2. The total spent on all boards is $149.22: 5.97x + 4.97y = 149.22

Now we solve the system of equations using either substitution or elimination method. For this example, we'll use the substitution method.

First, solve the first equation for y:
y = 26 - x

Now substitute y in the second equation:

5.97x + 4.97(26 - x) = 149.22

Expand and simplify this equation to find the value of x:

5.97x + 128.22 - 4.97x = 149.22

1x = 149.22 - 128.22

x = 21

Then, plug the value of x into the equation for y:

y = 26 - 21 = 5

So, Mr. Nall bought 21 units of 1x6 boards and 5 units of 2x6 boards.