Shoe price after 50% increase in sales and 25% revenue gain

[Oerg]

Homework Statement

On the first day, shoes in a shop were sold for $30 each. On the second day, the price of a shoe was reduced and the number of shoes sold on the second day increased by 50% while the money collected increased by 25%. Find the price of a shoe sold on the second day.

The Attempt at a Solution

well, I tried using an algebraic solution but got stuck. I used two unknowns, where

x=number of shoes sold on the first day
y=amount reduced for the price of a shoe sold on the second day.

I only managed to yield one equation from the problem which was not enough obviously,

amount collected on saturday:
$$1.5x(30-y)=30x\times1.25$$

please help, I must be missing another equation somewhere. Also, the final answer should be $25.

 

[Doc Al]

amount collected on saturday:
$$1.5x(30-y)=30x\times1.25$$

please help, I must be missing another equation somewhere.

Looks fine to me. (Note that one of your variables drops out.) Be sure to express the answer as the new price of the shoes, not the reduction in price.

 

[Oerg]

thanks doc ai I didn't realize one of my variables would drop out.