Question

A clothing store advertises that it is having a 25% off sale. for one day only, the store advertises and additional savings of 10%. use composition of functions to find the total percent discount. what would be the sale price of a $40 sweater?

Answer 1

Let assume x be the sale price

A clothing store advertises that it is having a 25% off sale.

The sale price with 25% discount is f(x) = sale price - 25% of sale price

f(x)= x - 0.25x = 0.75x

For one day only, the store advertises and additional savings of 10%.

The sale price with 10% discount is g(x) = sale price - 10% of sale price

g(x)= x - 0.10x = 0.90x

Use composition function

g(f(x)) = g( 0.75x) = 0.90(0.75x) = 0.675x

That is 0.675/100 = 67.5%

The total percent discount = 100% - 67.5% = 32.5%

what would be the sale price of a $40 sweater?

Here sale price x= 40

So we plug in 40 for x

g(f(40)) = g( 0.75(40)) = 0.90(0.75(40)) = 0.675(40) = 27

The sale price of sweater = $27