Question

Example 6

Answer 1

Answer:

The answer is below

Step-by-step explanation:

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?

Solution:

a) Let x represent the marked price and p(x) represent the price after discount. Since a discount of 15% is given, the price would be:

p(x) = $x(100\% -15\%)=x(1-\frac{0.15}{100} )=0.85x$

b) If x = discounted price and t(x) = total  cost with sales tax, then:

t(x) = $x(100\% +6.5\%)=x(1+\frac{6.5}{100} )=1.065 x$

c) Let t(x) represents the total  cost with sales tax

$t[p(x)] =p(x)+6.5\%\ of\ p(x) \\\\t[p(x)] = 0.85x+(0.065*0.85x)\\\\t[p(x)] =0.90525x\\\\for\ x=\ 3000:\\\\t[p(3000)] = 0.90525*3000=\ 2715.75$