LINEAR EQUATION THEATRE GROUP

Question

A theater group stayed in two cities. One hotel before tax was $500 higher than the first. The taxes at both hotels were 4.5%, and 4%. The tax paid for both was $423.75. How much did each hotel cost before tax?

Answer 1

x = 500 + y

x-y = 500

multiply by .04

.04x -.04y = .04(500) = 20

.04x + .045y = 423.75

.04x - .04y = 20

subtract the two equations to eliminate one variable, then solve the other variable

.085y =403.75

y = 403.75/.085 = $4750 hotel bill for the first hotel, before taxes

x = 4750+ 500 = $5250 hotel bill for the 2nd hotel, before taxes

check the answer

.04(5250) +.045(4750) = 210 +213.75 =423.75

UNLESS

.045x + .04y = 423.75

.04x - 0.4y = 20

.085x = 443.75

x = 443.75/.085 =5220.59

y =4720.59

.045(5220.59)+ .04(4720.59) = 234.93 + 188.82 = 423.75

then the before tax bills were $5,220.59 and $4,720.59

but odds are you want the 1st answers, if only because you get integer solutions

the problem is a little ambiguous as to which tax applies to which hotel