I need help solving this word problem

Question

A 72-foot piece of siding is cut into 3 pieces, so that the second piece is 3 times as long as the first piece, and the third piece is 5 times as long as the first piece. If x represents the length of the first piece, find the length of all three pieces.

Answer 1

I can help with this one!

Basically, you just go through the information they give you backwards. Let's use some basic Algebra to make this easier to read.

The problem gives us information related to the first piece, so let's make the first piece a, the second piece b, and the third piece c.

Also, it tells us that all three pieces added together is equal to 72.

Ok, let's go! The problem tells us that the second piece (b) is three times as long as the first piece (a), and the third piece (c) is five times as long as the first piece (a).

Translated into math:

b = 3a

c = 5a

Great! Now we can turn everything into terms of (a), which means we can solve the problem. Let's plug in our values for (a) that we did just now. Once we have the value for (a), we can figure out the values of (b) and (c).

72 = a + 3a + 5a

Since we can add all (a)s together, we get:

72 = 9a

Now, remember: the equals sign is a promise, a promise that both sides of an equation are the *same thing*. That means that when we do something to one side, we have to do the same thing to the other side. So how do we get (a) all by itself?

Easy! Divide both sides by 9, giving us:

8 = a

1/3 of the way there! Now let's plug this into our little mini-equations for (b) and (c).

b = 3a -----> b = 3 * 8

c = 5a -----> c = 5 * 8

b = 24

c = 40

a = 8

Ok, let's check our work by adding (a), (b), and (c) together. It should equal 72 if we did our work right.

72 = 8 + 24 + 40

72 = 72

Great! We did it!

Hope this helped.