Example 6

Rivera wants to purchase a riding lawn mower, which is on sale

17. USE A MODEL Mr. Rivera wants to purchase a

ainal price. The sales tax in his area is 6.5%. Let x represent the

for 15% off the original price. The sales tax ir

be lawn mower. Write two functions representing the price of

original cost of the lawn mower. Write two fu

after the discount and the price of the lawn mower t(x) after

the lawn mower p(x) after the discount and the price

a composition of functions that represents the price of the riding

sales tax. Write a composition of functions tha

wwer How much will Mr. Rivera pay for a riding lawn mower that originall

cost $1350?

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) = [tex]x(100\% -15\%)=x(1-\frac{0.15}{100} )=0.85x[/tex]

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

t(x) = [tex]x(100\% +6.5\%)=x(1+\frac{6.5}{100} )=1.065 x[/tex]

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

[tex]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[/tex]