Simple math word problem... can't grasp it

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I have a very simple problem in my book. I can't seem to get what I'm missing in their wording of the problem. here it is:
"A college bookstore purchased math textbooks for $54 each. At what price should the bookstore
sell the books if the bookstore wants to make a profit of 60% of the selling price?
Solution
Let's represent the selling price.
Selling price Equals Cost Plus Profit
s is the selling point
s = $54 + (60%)(s)
Solving this equation yields 135
The selling price should be $135."

I have no idea how this even makes sense. Maybe just don't understand the wording? Or maybe I don't understand profit?? Highly unlikely I feel like.

My obvious answer would be just 54 * 1.6. I'm not sure how 135 is 60% profit on 54, 135 is the price of the book made back, another 54 profit, and then the 60% of 54 on top of that. How is my book reaching this conclusion?

edit: looking back my obvious answer is wrong. I still am having troubles grasping this. Man I can self teach programming like nothing but trying to catch up on simple pre-algebra is a nightmare. Something about these incredibly simple word problems just shorts me out :/

edit: doh! I get it, 54 is 40% of the selling price, therefore giving a 60% gain in the overall price when selling at 135.

On another note, I'm terrified of the future if I can't even really understand what they are really trying to ask in simple problems like this... I tried to come up with a way to explain it to myself were I capable of going to the past, I'm not sure it would even be possible... Just something I apparently have to mull over til it clicks.

My initial reaction was to use 1.6 * cost, but they're asking for profit to be 60% of the selling price.

Well, no matter what, the profit is going to wind up being equal to: ($(Price) - $54
It's just that in this case, they want profit to also equal to: 0.6 * $(Price)

Using your terms, it gives the equation:
0.6 * s = s - $54

Yeah... these worded questions always boggle my mind.

"A college bookstore purchased math textbooks for $54 each. At what price should the bookstore sell the books if the bookstore wants to make a profit of 60% of the selling price?

The trick is you have to work out 60% of the selling price:

selling price - cost = profit

profit = 60% of selling price

let s represent the selling price


so

s - $54 = 0.6s

-> s - $54 + $54 = 0.6s + $54 = $54 + (60%)s (as per your book)

-> 1s - 0.6s = $54 + 0.6s - 0.6s

-> 0.4s = $54

-> s = $54/0.4 = $135

Hope this helps )

Sorry vet, I didn't notice you'd already replied

That's no problem at all, you actually explained it more throughly and without typos lol.

First let's work backwards to understand what the expression for the sale price is actually saying.

s=54+0.6s and the solution says s = 135, then the equation says, 135 = 54 + some percentage of 135 which is less than 135 itself.

Now with that in mind, working forwards, let's say you are the bookstore and you bought a book for $54 dollars and want to sell it such that your profit is some percentage of what you sold it for.

A general expression for profit is p = sold for - bought for. We know you bough the book for $54 so
p= sold for - 54

In this case, we want our profit to also be some percentage, x, of what we sold it for. So p = x * sold for

Equating both p's

x * sold for = sold for - 54

Let's called "sold for" s.
xs = s - 54

We can test to make sure this is correct. Let's say we bought the book for $54 and sold it for $54. That means we broke even and make no profit, so our profit was 0% of the sale price. We can plug these values in to both sides of the equation. If our equation is correct, the sides will be equal.

Let x = 0 and s = 54

0*54 = 54-54
0 = 0

Ok, our equation works.

Now let our profit be 60% of the sale price, and the sale price be what we are solving for.

0.6s = s - 54

Rearranging to solve for s....

0.6s - s = - 54

- 0.4 s = - 54

54 = 0.4s

54/0.4 = s

135 = s

Does the logic make sense now or is it more confusing?