Jim buys a bike that is on sale for 25% off the original price. The original price is $120 more than the sale price. What is the original price of the bike?

sale price is .75 the original price. so,

.75p + 120 = p

or, the discount is the difference in prices.
.25p = 120

Sale price = $X.

Original price = x + 120.

x = 0.75(x+120).
x = 0.75x + 90,
0.25x = 90,
X = $360.
x + 120 = 360 + 120 = $480 = original price.

To find the original price of the bike, we can work backward from the information given. Let's break down the problem step by step:

1. Let's assume the sale price of the bike is represented by "x".

2. According to the problem, the bike is on sale for 25% off the original price. This means Jim pays 75% (100% - 25%) of the original price, which is given as $120 more than the sale price.

3. So, the equation to represent this situation is: 0.75 * "original price" = "sale price" + $120.

4. Replacing "sale price" with "x" in the equation, we get: 0.75 * "original price" = x + $120.

5. Now, we can solve this equation to find the original price.

Let's proceed with the calculations:

0.75 * "original price" = x + $120.

Simplifying, we have:
0.75 * "original price" = x + $120.

Now, let's substitute the given value of "x" into the equation.

0.75 * "original price" = x + $120.
0.75 * "original price" = $120 + $120.
0.75 * "original price" = $240.

To isolate "original price," we can divide both sides of the equation by 0.75:

("original price") = $240 / 0.75.

Calculating the division, we find:
("original price") = $320.

Therefore, the original price of the bike is $320.