1. COST Mr. Rivera wants to purchase a riding lawn
mower, which is on sale for 15% off the marked price.
The store charges sales tax 6.5% on all sales. Write a
function p(x) that represents the price after a 15%
discount. Write a function t(x) that represents the total
cost with sales tax. Write a composition of functions that
represents the total cost of a riding lawn mower on sale.
How much will Mr. Rivera pay for a riding lawn mower
that has a marked price of $3000?

1 answer

Question:

1. COST Mr. Rivera wants to purchase a riding lawn
mower, which is on sale for 15% off the marked price.
The store charges sales tax 6.5% on all sales. Write a
function p(x) that represents the price after a 15%
discount. Write a function t(x) that represents the total
cost with sales tax. Write a composition of functions that
represents the total cost of a riding lawn mower on sale.
How much will Mr. Rivera pay for a riding lawn mower
that has a marked price of $3000?

Answer:p(x) = 0.85xt(x) = 1.065x(t o p)(x) = 0.9x$2700Step-by-step explanation:If the marked price is $x, then the function p(x) that gives the price of the riding lawn mower after 15% discount will be [tex]p(x) = x(1 - \frac{15}{100}) = 0.85x[/tex]where x is the marked price.Now, the function that gives the total cost with sales tax will be given by [tex]t(x) = x(1 + \frac{6.5}{100}) = 1.065x[/tex]where x is the discounted price.Therefore, the composite function that gives the total cost of the riding lawn mower on sale is given by (t o p)(x) = 1.065(0.85x) = 0.9x ............ (1)where x is the marked price.If the marked price x = $3000, then Mr. Rivera has to pay for the riding lawn mower, from equation (1),(t o p)(3000) = 0.9 × 3000 = 2700 dollars. (Answer)

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