Math Challenge Problem

Question

The question is below:

In August, September and October, POTW Motors paid a constant price of 1.25 dollars per liter of fuel. In September, they used $x$% more litres of fuel than in August, where $x$ is some positive number. In October, they used $x$% less litres of fuel than in September. The bookkeeper for POTW Motors forgot to record how much the company paid for fuel in September. However, she does know that POTW Motors paid a total of $3125 for fuel in August and 3080 dollars for fuel in October. Determine POTW Motor’s total fuel cost for September.

How I went on attempting this question was by using two equations.

Let y represent the fuel used in litres in September`

After the two equations I used were

$2500(1+x/100) = y$

$2464(1-x/100) = y$

After solving this system for $x$ I am getting a different solution than what is the right one. I would like some guidance about where I went wrong?

EDIT 1: Thanks to Eclipse Sun for pointing out a mathematical error.

Answer 1

$Aug * 1.25 = 3125 \implies Aug = 2500$.

$Sep = Aug \cdot \left(1 + \frac{x}{100}\right)$

$Oct = Sep \cdot \left(1 - \frac{x}{100}\right) = Aug \cdot \left(1 + \frac{x}{100}\right) \cdot \left(1 - \frac{x}{100}\right) = Aug \cdot \left(1 - \frac{x^2}{10000}\right)$

We have that $Aug \cdot \left(1 - \frac{x^2}{10000}\right) * 1.25 = 3080 \implies Aug \cdot \left(1 - \frac{x^2}{10000}\right) = 2464$. Substituting $Aug = 2500$, we have $\left(1 - \frac{x^2}{10000}\right) = 0.9856$, giving us $x = 12$. Fuel cost for September = $2500 * 1.12 * 1.25 = 3500$.

I get the answer to be $3500$.