Please HELP! Answer this problem

Question

Shawn is starting a woodworking project for which he needs a large number of 2x4s. He plans to buy 2x4s that are 6 feet in length and cut them into the following sizes:

1. eight pieces that are 12.5 inches long
2. six pieces that are 8.75 inches long
3. nine pieces that are 6.25 inches long

Note: A 2x4 ("two by four") is a rectangular piece of wood that is two inches high and four inches wide, as shown in the picture. It can have varying lengths. The 2x4s that Shawn is buying have a length of 6 feet, or 72 inches.

Find the most efficient way for Shawn to cut these pieces. In other words, what is the fewest number of boards he can cut from?

Describe for Shawn the most efficient way to cut his boards. You may include a diagram if you wish.

Answer 1

First, it might be helpful to find the total amount that he needs.

8*12.5=100 inches

6*8.75=52.5 inches

9*6.25=56.25 inches

100+52.5+56.25=208.75 inches

Shawn needs at least 208.75 inches of wood.

By taking the 208.75 total inches and dividing by 72 inches (the length of each board), we find out that he needs 3 boards. Now some arrangements need to be made to figure out what pieces to cut from the boards. There are multiple different ways to cut the boards, but this is one possible solution:

5(12.5)+1(8.75)=71.25

5(8.75)+2(12.5)=68.75

9(6.25)+1(12.5)=68.75