Math Word Problem with multiple percentages

Question

I've completely forgotten how to do these problems, and State Testing is coming up, so I want to be sure I know this. 

 

Bob pays $13.25 for a shirt. That price includes a 10% tax. The shirt is 25% off its original price. How much did the shirt originally cost?

Answer 1

(0.75p)(1.10) = 13.25 is what you have described, where p would be original price. The factor 1.10 reflects incorporation of 10% tax into the out-the-door cost paid by Bob.  Solve for p.

Answer 2

Bob pays $13.25 for a shirt. That price includes a 10% tax. The shirt is 25% off its original price. How much did the shirt originally cost?

 

let x = original cost of the shirt 

25% off is another way of saying you're paying 75% of the original cost. (1 - 0.25 =0.75) Less than 100% of the item cost.

10% tax is applied to the amount you are paying. (ie. discounted shirt price, 75% the original cost of the shirt)

The 10% tax is an added amount, just like saying you are paying 110% of the discounted shirt price. 100% is the item cost, + 10% tax (1 + 0.1 = 1.1)

 

13.25 = 1.1(0.75x)

 

13.25 = 0.825x

 

13.25/0.825 = x

 

16.06 = x

 

Check and see if it makes sense.

 

16.06 - 0.25(16.06) = 12.04

 

after tax

 

12.04 + 0.1(12.04) = 13.25