Math

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 4% , and the tax in the second city was 7% . The total hotel tax paid for the two cities was $455 . How much was the hotel charge in each city before tax?

Please help me follow the steps. I understand that you have to put the two cities in equations and solve but the numbers confuse me. the total of the two cities and the number earned.

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  1. first hotel charge ---- $x
    2nd hotel charger ---- $x+1000

    .04x + .07(x+1000) = 455
    how about multiplying each term by 100 if you don't like decimals

    4x + 7(x+1000) = 45500
    11x + 7000 = 45500
    11x = 38500
    x = 3500

    first hotel cost $3500
    2nd hotel cost $4500

    check:
    .04(3500) + .07(4500) = 455

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  2. A theater group made appearances in two cities. The hotel charge before tax in the second city was $500 higher than the first. The tax in the first city was 8.5% and the tax in the second city was 4%. The total hotel tax paid for the two cities was $613.75. How much was the hotel charge in each city before tax?

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