# Thread: Make an equation and find the two prices of the shoes

1. ## Make an equation and find the two prices of the shoes

Hello! I would like some help with this task.
Two manufacturers make "elevator shoes" for disco dancing of different qualities and the higher quality shoes sells for 8£ more than the others. As a shoekeeper, if you bought the cheaper type you could get five more pairs for £240. What are the prices of the two shoe types?

Thank you!

2. Haven't you been asking similar questions already? Try to have an attempt yourself.

Let the cheaper variety of shoe $\displaystyle = x$ and the more expensive type be $\displaystyle y$.

You know that $\displaystyle x + 8 = y$ (the more expensive shoes '$\displaystyle y$' cost 8 pounds more than the less expensive '$\displaystyle x$') . What else do you know?

Use this:
if you bought the cheaper type (x) you could get five more pairs for £240

3. This is my attempt, however the answer are incorrect.
x+5x=240
6x=240
x=40

4. The wording is strange, granted. I think they mean that 5 pairs of 'x' cost 240 pounds. So $\displaystyle 5x=240$ Then $\displaystyle x=48$. Does that match their answer?

5. Originally Posted by Anna55
Hello! I would like some help with this task.
Two manufacturers make "elevator shoes" for disco dancing of different qualities and the higher quality shoes sells for 8£ more than the others. As a shoekeeper, if you bought the cheaper type you could get five more pairs for £240. What are the prices of the two shoe types?

Thank you!
Let "x" be the price of the cheaper type of shoe, in pounds. Then the more expensive pair is x+ 8 pounds
The number of cheaper shoes you could buy for £240 is 240/x. The number of more expensive pairs is 240/(x+ 8). Saying that you could get 5 more of the cheaper shoes means that 240/(x+8)- 240/x= 5.

6. Thank you HallsofIvy, I understand now. However I believe that the equation should be like this: 240/(x+8)-5 = 240/x