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# the complete hotel bill was \$68 (room and tax). If the sales tax is 9%, what was the cost for the room before the tax?

have been setting up word problems as proportions but i cant seem to get this one right.

### 3 Answers by Expert Tutors

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
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C - Cost of Hotel    r = Tax rate

C + C r = C ( 1 +r)

C (1 + 0.09 ) = \$68

C = \$68/1.09 = \$62.39
Zakiyyah M. | Expert Math, Physics, and Engineering Tutor! Let's Succeed Together!Expert Math, Physics, and Engineering Tu...
5.0 5.0 (93 lesson ratings) (93)
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Here is another approach with a lot of detail.

Let x = cost of the room before taxes (since this is what we want to find, let it be x.  This is good practice for all word problems)
9% tax is equivalent to .09 (removing the percent sign and replacing with 9/100  because 9% = 9/100)
\$tax = .09x

68 it total cost of the room plus total tax simply put:

\$68 = \$room + \$tax (note that tax in this equation is the dollar amount, not the percentage of tax)

So that means

x+ (.09x) = 68  or  ( × + (9/100)x = 68)

1x+ .09x = 68
1.09x = 68  (divide both sides by 1.09)

x = 68/1.09

x = 62.385 (round to the nearest 100th because it's money. Money only goes out 2 decimal places.  So round UP because the last number is 5)

x = \$62.39  FINAL ANSWER

\$tax = 62.39*.09 = 5.62
\$room + \$tax = \$68
\$62.39 + \$5.62 = 68.01 (close enough.. because of rounding it's a little off... but still correct)

The reason Bam's answer is wrong is because the 9% is based off of the cost of the room BEFORE taxes.  This is a common mistake in calculating taxes.  Always remember that taxes are based off the ORIGINAL cost, not final.

Hope that helps.

Zakiyyah

Not true Bam . Problem Explicitly says:

The bill was issued for \$68 ( Room and TAX) , means Room Plus Tax , and the bills normally issued on total amount,including tax.
Bam K. | Multi-discipline, Passionate, and Compassionate TutorMulti-discipline, Passionate, and Compas...
4.5 4.5 (12 lesson ratings) (12)
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room and tax minus tax = room before tax

\$68 - 9% of \$68 is the cost of the room before tax : that is \$68 x (1 - 0.09) = \$68 x (0.91) = \$61.88

ATTENTION! PARVIZ'S ANSWER IS NOT CORRECT!