Math work of people math math...

Question

If a item costs $39.95 for 25% off with a 7.5% tax what's the sales price and total cost

Answer 1

Think about it like your grocery receipt. The item you bought was 25% off and you paid 7.5 % tax on it. 

 

Write it out like it's a receipt if that helps you visualize the problem.

 

Ex: 

      PS3.    100

25% off.    -25

-----------------------

subtotal.     75

tax 7.5%   5.63

 

total           80.63

 

 

Now if we think about the question using the fake receipt above it helps to think about the problem.

 

 

So we know the final total is 39.95. Staring here we can work backwards.

 

To find 7.5% of something you have to multiply it by 0.075.

 

x*0.075 + x = 39.95

 

The x is the subtotal of the item purchased. So we have to multiply it by the tax and then add it to the subtotal to find our total of 39.95.

 

Now combine like terms and solve for x

 

x*1.075 = 39.95

 

x = 37.16

 

Now we have our subtotal. We know the item was 25% off so we can find the original price the same way we found the subtotal. But since it is a discount to the original price we set up the equation differently. We are subtracting from the original cost.

 

x is now going to be the original price

 

x - x*0.25 = 37.16

x*0.75 = 37.16

x = 49.55

 

so original price is 49.55

 

 

Answer 2

Let x = original price

 

Then sale price = x - 0.25x = 0.75x

 

0.75x + 0.075(0.75x) = 39.95

 

0.80625x = 39.95

 

              x = $49.55

 

Original price = $49.55

 

Sale price = 0.75(49.55) = $37.16

 

Sales tax = 0.075(37.16) = $2.79