multi-step problem: At what price is B equal to A?

[pcpolivick]

Here is the problem:

Company A offers a 25% discount. Company B offers a 35% discount on anything over $50.00. At what price does Company B offer the same discount as Company A? Solve algebraically.

I'm not exactly sure how to set up the problem. If someone could just get me started that would be so great. I'm an accounting studen at an online university.
Thanks a bunch!

 

[o_O]

Say that Company A sells the product at price Y (without the discount). What would the discount be then?

Similarly, if Company B sells the product at price X (without the discount), what would the discount be (if X > $50 of course)?

Once you set these two expressions equal to each other, you can see that there can be many solutions.

 

[Mrspi]

Re: multi-step problem

Here is the problem: company A offers a 25% discount. Company B offers a 35% discount on anything over 50.00 at what price does company B offer the same discount as Company A. Solve Algebraically.
I'm not exactly sure how to set up the problem. If someone could just get me started that would be so great. I'm an accounting studen at an online university.
Thanks a bunch!

Let x = dollar amount of sales

With company A, you get a 25% discount on all sales, so your discount is 0.25x

With company B, you get a discount of 35% on any amount OVER $50. So there's no discount on the first $50, but after that, you get a discount of 35%. Your discount with company B is 0.35(x - 50)....of course, this is only valid if the amount of sales is $50 or more.

Now...you are asked what amount of sales would give you the same discount for both companies. So, when is

discount with company A = discount with company B

0.25x = 0.35(x - 50)

Solve that for x....