Question 361922: You go to a local mechanic to get your tires changed. The tires cost $300. There is a 6% sales tax, but you get a 10% discount. There is also a $10 non-taxable disposal fee for your old tires, which the mechanic tells you is not subject to discount.
Write a function, t(x) for the total purchase amount after taxes but before discounts and fees.Does it matter whether the mechanic adds the tax first or takes the discount first?
I really need some help with this problem everything I have tried hasn't been right.
Found 2 solutions by mananth, Theo:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! tyre = $300
let x be the tyre cost
tax = 6%
function with no discount and fees
t(x)= x+0.06x
...
BEFORE DISCOUNT
Price 300 add 6% tax = 318
discount 10% = 31.8
318-31.8=$286.2
..
AFTER DISCOUNT
price = 300
10% discount
price = 300-30=270
270*1.06 =286.2
..
how does it matter ?
m.ananth@hotmail.ca
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m.ananth@hotmail.ca
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! tires cost $300.
6% sales tax.
10% discount.
$10 disposal fee for old tires not subject to discount.
your formula if the discount is applied first would be as follows:
x = cost of the tires.
t(x) = (.9*x + 10) * 1.06
if x = 300, then the cost is (.9*300 + 10) * 1.06 = (270+10)*1.06 = 280*1.06 = $296.80
if the tax is applied first and then the discount is applied, your formula would be as follows:
t(x) = (x+10)*1.06 - (.1*x)
if x is equal to $300, the cost is $310*1.06 - .1*300 = = $328.60 - $30 = $298.60.
you pay more if the tax is applied first.
your discounted price of .9*x stems from x - .10*x which becomes (1-.10)*x which becomes .9*x
your cost with tax stems from y + .06*y = (1 + .06)*y = 1.06*y.
y is the amount of the cost that is taxed.
if the discount is applied first, then y is equal to (.9*x + 10).
if the discount is applied after, then y is equal to (x+10).
so we'll go through it again, just to make sure you understand what is happening.
cost is 300.
apply discount first and the cost is 270.
add 10 to make the total cost 280.
tax 6% * 280 + 280 = 296.8
tax first and the cost without the discount is 300 + 10 = 310.
tax 6% * 310 + 310 = 328.6
subtract discount of 30 to make a total of 298.60.
the difference in the tax you paid is the difference of the tax on the undiscounted price versus the tax on the discounted price.
the difference is 298.6 - 296.8 = 1.80
.06 * 30 = 1.8
the difference is the tax on the discount.
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