Answer:
p(x) = 0.85x
t(x) = 1.065x
(t o p)(x) = 0.9x
$2700
Step-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)
Mr. Rivera would pay $2715.75 for a riding lawn mower that has a marked price of $3000
Let x represent the marked price. Let P(x) represent the price after a 15% discount and T(x) represents the total cost with sales tax.
P(x) = x - 15% of x
P(x) = 0.85x
T(x) = P(x) + tax = P(x) + 6.5% of P(x)
T(x) = 0.85x + 0.05525x
T(x) = 0.90525x
For a marked price of $3000:
T(3000) = 0.90525(3000) = $2715.75
Mr. Rivera would pay $2715.75 for a riding lawn mower that has a marked price of $3000
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