Four feet less than twice its width? what does this mean? can i get the formula and steps?

Let's get a feel for what information we need for this problem. We ultimately want to find the dimensions of the mural. What we know are

Let's see how this information can help us through the different parts of the problem.

A good place to start is with naming our variables so we can start to put together equations. Let's call our length l and our width w. We're told that l is "four feet less than twice" w, or symbolically:

l = 2w - 4

Any time we have to use an l, we're now able to substitute the expression 2w - 4 instead.

Again, let's start with giving our function a name. If we call the area of the mural A, we use the abbreviation A(w) to mean "A as a function of w," or "A of w" for short.

We know that the area A of a rectangle is normally just its length times its width - A = lw - but sense we want this function as a function of w alone, we can replace l with the expression 2w - 4 from earlier to give us

A(w) = (2w - 4)w = 2w² - 4w

We're finally ready to tackle this problem's main question. Our function from the last section tells us what the area of the mural is entirely in terms of w, and the first section tells us how to find l if we already know w. Going back to one of the first bullet points, we also know that the area of the mural is 70 ft², so we can say that we want to know what w is when A(w) = 70, or equivalently, when

2w² - 4w = 70

To solve for w, we can first divide away a 2 on either side, leaving us with

w² - 2w = 35

or equivalently,

w(w - 2) = 35

The only value w can be to make this true is 7, since 7(7 - 2) = 7(5) = 35, so we know that the width must be 7 ft. The area is 70 ft², so the length of the mural must be 10 ft., since 7 x 10 = 70.

22 dimes and 9 nickels

step-by-step explanation: