Question

a theater group made appearances in two cities. the hotel charge before tax in the second city was $1000 higher than in the first. the tax in the first city was 5%, and the tax in the second city was 6.5%. the total hotel tax paid for the two cities was $668.75. how much was the hotel charge in each city before tax?
first city: $
second city: $

Explanation:

Step1: Define variables

Let $x$ = pre-tax charge (1st city).
Let $x + 1000$ = pre-tax charge (2nd city).

Step2: Set up tax equation

Tax from 1st city: $0.05x$
Tax from 2nd city: $0.065(x + 1000)$
Total tax equation:
$$0.05x + 0.065(x + 1000) = 668.75$$

Step3: Expand and simplify

$$0.05x + 0.065x + 65 = 668.75$$
$$0.115x + 65 = 668.75$$

Step4: Isolate variable term

$$0.115x = 668.75 - 65$$
$$0.115x = 603.75$$

Step5: Solve for $x$

$$x = \frac{603.75}{0.115}$$
$$x = 5250$$

Step6: Find 2nd city charge

$$x + 1000 = 5250 + 1000 = 6250$$

Answer:

First city: $\$5250$
Second city: $\$6250$