SAT math help, please?

Question

The price of a telephone was first increased by 10 percent and then the price was decreased by 25 percent. The final price was what percent of the initial price?.
how do you solve that question. I know that the answer is 82.5% but I don't know the way to solve it.
please explain it to me like I'm 9 years old.
thanks in advance.

Answer 1

The easiest way to do this in an easy way to understand is to pretend that you have 100 dollars and do the math:

$100 + 10% = $110

$110 - 25% = ???

25% of $110 is $27.50 so subtract this from $110.

$110 - $27.50 = $82.50

Answer 2

Increasing 10% is like multiplying by 1.1 (100% + 10% = 110% = 1.1). Decreasing by 25% is like multiplying by .75 (100% - 25% = 75% = .75).

So say the initial price was 100. It then changes to 100*1.1 = 110 and is reduced by 110 * .75 = 82.5. So it's 82.5 out of 100, or 82.5%

Answer 3

(1 + .10)x = 1.10x

1.1(1 - .25)x = 1.1(.75)x = .825x

ANS : 82.5%

first i increase the original unknown price by 10%, which gave me 1.1x , now this has become the new price, then i decreased that value by 25%, which gave me .825 or 82.5%.

Answer 4

for the price of telephone, set it equal to x

initially, the price was increased by 10 percent, so the price would be x + .1x

Then the price decreased by .25 percent, so it would be equal to (x + .1x) - (0.25x + x) so the x's cancel out, and youre left with 0.1x - 0.25x, which is equal to -.15x which would mean the final price was 85% of the first price

Answer 5

let x be the original price (it really doesn't matter, but it makes it easier to see)
increase by 10%. New price=x+.1x=1.1x
decreased by 25% or .25*1.1x=.275x
new price is 1.1x-.275x=.825x or 82.5% of the original.