Question

A hotel manager found that his gross recipients for the day, including a 7% sales tax, totaled to $3479.64. Find the amount of sales tax collected.

(I ask for someone to please, quickly, help me answer he question, I can't seem to properly do it myself.)

Answer 1

$227.64

Explanation:

The relevant relations are ...

sales + tax = total

tax = 7% × sales

Using the second equation, we can write sales in terms of the tax as ...

sales = tax/0.07

Substituting this into the first equation gives ...

tax/.07 + tax = total . . . . . substitute for sales

tax(1/0.07 + 1) = total . . . . factor out tax

tax ((1 +.07)/.07) = total . . . simplify to a single fraction

Multiply by the inverse of this fraction:

tax = .07/1.07 × total = (7/107)($3479.64)

tax = $227.64