Here is one on the SAT practice tests that is a good example of the percent increase/decrease type of problem:

Edward bought a smartphone at a store that gave a 20% discount off its original price. The total amount he paid to the cashier was P dollars, including an 8% sales tax on the discounted price. What was the original price of the smartphone in terms of P?

SOLUTION:

Use a variable, such as X, for the original price. Then set up an equation and solve for X, the original price of the smartphone.

We know that Edward bought the phone for 20% off original price, or 0.8X; and that he paid 8% tax on that. Add those together to get the price P he paid:

0.8X    +     0.08(0.8X)    =     P

This results in X  =  1.15P, however...

Here it is preferable to factor out the 0.8 rather than combine like terms, as you’ll see:

0.8(1X  +  0.08X)  =   P

0.8(1.08X)    =    P

X    =        P/[(0.8)(1.08)]

This is the answer choice given on the practice test, rather than 1.15P, which would be the simplest (or even P/0.864). Seeing the factoring option would therefore save you some time and/or confusion.

 

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