A jacket costs 4 times as much as a shirt. If the total cost of the jacket and short is $280, how much does the shirt cost?

Answer 1

The most common use of Algebra is translate word problems into the actual equation you need to find the solution for, and also the one thing that people find the hardest.

Looking at the word problem given here, we are trying to find the cost of a shirt and jacket, that much is obvious, and we know the total of them together - $280. What else do we know? We know that the jacket costs 4 times as much as the shirt. Ok, then how do we translate all of this into an equation to find the cost of the shirt?

Let's start with the shirt and jacket. We know that the jacket costs 4 times as much as the shirt; if we say that the shirt costs some unknown value x, then the jacket must cost 4 times that, or 4x. We know that the total of these two together is $280, that must mean if we add them, we'll get the total, so:

x + 4x = $280

Now we have our equation! We can start to solve for x. First, combine like values to get:

5x = $280

Now solve for x, and to do so, we must get x all by itself. This is a balanced equation (the clue is the equal sign) which means that anything we do to one side, we can and must do to the other. If I divide 5x by 5, I get 5x/5 which reduces to 1 (because anything over itself is equal to 1) and this achieves our goal of isolating the x. However, if I divide the left side by 5, I must to the same for the right side. 280/5=56, which leaves us with:

x=$56

That's an expensive shirt!

Let's prove it's correct:

The shirt ($56) + the jacket (four times the shirt - 4x$56 - $224)

$56 + $224 = $280

Success!