How to solve simple Percentages problem?

[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.

Please help.

[tiny-tim]

Hi vitaminZ ! Welcome to PF! :smile:
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?
…
I know Q1 is wrong too. I don't know how to solve questions that are worded in english like this.

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 :wink:)

(Always multiply, never divide!)
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%)
…
I don't know how to find the "percentage price reduction".

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? :smile:

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 :wink: