Question

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. 18. Write a function, t(x) for the total purchase amount after taxes, ignoring any discounts and fees.

Answer 1

Answer:

X= cost of the tires

t(x)= (.9*X+10)*1.06

If x = 300, then the costo is (.9*300 + 10) *1.06 = (270 + 10)* 1.06 = 280 * 1.06 = $296.80

If the tax is appplied first and then the discount is applied, your formula would be:

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 mor if the tax is applied first.

Your discounted price of .9*x stems from x - .10*x which becomes (1-.10)*x wich becomes .9*x

Your cost with tax stems from y + .06*x =(1+.06)*y = 1.06*y

Y is the amount of the cost that is taxed.

if the discuount is applied first, then y is equal to (.9*x + 10)

if the discount is applied after, then y is equal to (x+10).

The difference is the tas on the discount

Explanation:

Answer 2

Answer:

$t(x)= x+0.06x$

or

$t(x)= 1.06*x$

Explanation:

if we take x as the tyre cost ($ 300)

Tax = 6%

the function ignoring the discounts and fees would be:

$t(x)= x+0.06x$

Now including discounts and fees, can be done by two ways

1) adding taxes before discount

To the price 300 add 6% tax = 318

discount would be 318 * 10% = 31.8

then the cost is 318 - 31.8 = 286.2

2) adding taxes after discount

To the price (300) we will apply the 10% discount

discount would be 300 * 10% = 30

price now will be 300- 30 = 270

now to the calculated price add the 6% tax

270* 1.06 = 286.2