# How to solve simple Percentages problem?

1. May 29, 2010

### vitaminZ

1. The problem statement, all variables and given/known data
Q1. A shop's normal price for a camera is $175. If prices are temporarily reduced by 7.5%, what is the new price of the camera? Q2. In a sale, a shop reduces its prices by the amount of the VAT on each item. If VAT is 17.5%, what is the percentage price reduction? (Hint: The answer is not 17.5%) 2. The attempt at a solution Q1. 7.5+100 /100 = 1.075$175 /1.075 = $162.79 Q2. I assume item x =$100
VAT = 17.5% of $100 =$17.5 on that item
To find price before VAT = 100+17.5 /100= 1.175
100 /1.175= $85.11 100-85.11 =$14.89

I don't know how to find the "percentage price reduction". The reduction in absolute terms seems to be $14.89 on a$100 item. And I know Q1 is wrong too. I don't know how to solve questions that are worded in english like this.

2. May 29, 2010

### tiny-tim

Welcome to PF!

Hi vitaminZ ! Welcome to PF!
In English, "reduced by 7.5%" means that the new price is (100 minus 7.5)/100, = 0.925.

So to reduce the price by 7.5%, you multiply it by 0.925 (check, and you'll see that this is not exactly the same as dividing by 1.075 )

(Always multiply, never divide!)
If the basic price is $100, then the VAT is$17.5, so the total price is $117.5. "percentage price reduction" means the fraction (as a percentage) by which you must reduce the total price to get the reduced price (ie, the basic price, without the VAT) … ie by what fraction must you reduce 117.5 to get 100? So … your answer is very nearly complete, except … i] you should keep "x" as "x", not make it 100 ii] your fractions are dollars/dollars, which is just a number (ie, don't write "$14.89", write "14.89%", or "0.1489")

iii] it would be quicker to use the difference (\$17.5) to make the fraction