Math college algebra 1

Question

A theatre group made appearances in two cities. The hotel charge before tax in the second city was $1000 higher than in the first city. The tax in the first city was 4.5%. the total hotel tax paid for the two of cities was $465. How much was the hotel charge in each city before tax?

Answer 1

S=F+1000

.045S +tF = 465

There's 3 unknowns just 2 equations, with no unique solution.

an infinite number of possible solutions

S=Second city's hotel charge before tax

t = tax rate on First city's hotel charge

F = First city's hotel charge before tax

Let t = 5.5% = .055, a tax in a reasonable range

then

.045S + .055(S-1000) = 465

.45S +.055S = 465 +55 = 520

S = 520/.1 = $5200 hotel charge before tax in Second city

F = $4200 hotel charge before tax in First city

.045(5200) + .055(4200)

= 234+231

= 465