Maria is staying at a hotel that charges $99.95 per night plus tax for a room. A tax of 8% is applied to the room rate, and an additional onetime untaxed fee of $5.00 is charged by the hotel. Which of the following represents Maria's total charge, in dollars, for staying x nights? (99.95+0.08 x)+5 1.08(99.95 x)+5 1.08(99.95 x+5) 1.08(99.95+5)x

Question

Maria is staying at a hotel that charges  $99.95 per night plus tax for a room. A tax of  8% is applied to the room rate, and an additional onetime untaxed fee of  $5.00 is charged by the hotel. Which of the following represents Maria's total charge, in dollars, for staying  x nights?  (99.95+0.08 x)+5  1.08(99.95 x)+5  1.08(99.95 x+5)  1.08(99.95+5)x

Bytelearn · Accepted Answer

Rephrase the Problem: First, let's rephrase the  ＂What is Maria's total charge for staying x nights at a hotel with a nightly rate of $99.95, an 8% tax, and a one-time untaxed fee of $5.00?＂Calculate Room Cost: Calculate the total room cost for x nights before tax. This is done by multiplying the nightly rate by the number of nights. Total room cost before tax = $99.95 * xCalculate Tax: Calculate the tax on the total room cost. Since the tax rate is 8%, we multiply the total room cost before tax by 0.08. Tax amount = Total room cost before tax * 0.08 Tax amount = $99.95 * x * 0.08Add Tax to Room Cost: Add the tax amount to the total room cost before tax to get the total room cost after tax. Total room cost after tax = Total room cost before tax + Tax amount Total room cost after tax = $99.95 * x + ($99.95 * x * 0.08)Simplify Total Cost: Simplify the expression for the total room cost after tax by factoring out the common factor of $99.95 * x. Total room cost after tax = $99.95 * x * (1 + 0.08) Total room cost after tax = $99.95 * x * 1.08Add One-Time Fee: Add the one-time untaxed fee of $5.00 to the total room cost after tax to get Maria's total charge. Maria's total charge = Total room cost after tax + One-time fee Maria's total charge = ($99.95 * x * 1.08) + $5.00Examine Given Options: Now, let's examine the given options to see which one correctly represents Maria's total charge for staying x nights.  Option 1: (99.95+0.08 x)+5 This option is incorrect because it adds the tax rate to the nightly rate before multiplying by the number of nights, and it also incorrectly adds the one-time fee inside the parentheses.  Option 2: 1.08(99.95 x)+5 This option correctly applies the tax to the total room cost before adding the one-time fee, which matches our calculation.  Option 3: 1.08(99.95 x+5) This option incorrectly applies the tax to the sum of the total room cost and the one-time fee, which is not taxed.  Option 4: 1.08(99.95+5)x This option incorrectly applies the tax to the nightly rate plus the one-time fee before multiplying by the number of nights, which is not how the tax is calculated.  The correct representation of Maria's total charge for staying x nights is given by Option 2.

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