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.)
Accepted Solution
A:
Answer: $227.64Step-by-step explanation:The relevant relations are ... sales + tax = total tax = 7% × salesUsing the second equation, we can write sales in terms of the tax as ... sales = tax/0.07Substituting 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 fractionMultiply by the inverse of this fraction: tax = .07/1.07 × total = (7/107)($3479.64) tax = $227.64