Suppose a friend tells you she paid a total of $8,540 for a motorcycle, and you'd like to know the motorcycle's list price (the price before taxes) so that you can compare prices at various dealers. Find the list price, p, of the motorcycle if your friend bought the
motorcycle in:
a) Washington, where the sales tax is 6.5%.
b) Idaho, where the sales tax is 6.0%.
C) A state where the sales tax is r. Assumer is in decimal format.
d) Solve for r in your answer to (c) above

a) $8018.78

b)   $8056.60

c)  8540 / (1+r)

d)  r = (8540/x) - 1 where "x" is the list price.

Step-by-step explanation:

Recall that the:

total price paid = list price + sales tax

total price paid = list price + percent * list price

a) then, in Washington:

8540 = x + 0.065 * x

8540 = x (1 + 0.065)

8540 = x (1.065)

x = 8540 / 1.065

x = $8018.78

b) in Idaho where the sales tax is 6.0% we do a similar calculation but using the decimal form of the percent 0.06:

8540 = x (1 + 0.06)

8540 = x (1.06)

x = 8540 / 1.06

x = $8056.60

c) If the percent tax is "r" then:

we do:

8540 = x (1+r)

x = 8540 / (1+r)

d) solving for "r" instead of for "x":

8540 = x (1+r)

divide by "x" (the list price):

(8540/x) = 1 + r

subtract 1 from both sides:

(8540/x) - 1 = r

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .