Question

Rachel pays $131.44 for a desk, including tax. The tax is 31 cents less than 1 16 the desk's price. What is the price for the desk before adding the tax?
A) $116.00

B) $118.00

C) $122.00

D) $124.00

Answer 1

Let D represent the cost of the desk and T represent the tax paid.

Given,the cost of the desk plus the tax equals $131.44, so equation becomes

D + T = 131.44    ...(1)

As given, tax T equals 1/16 times the cost of the desk less 0.31 dollars, so equation becomes T = (1/16)D - 0.31

Now substituting the right side of this equation for T into equation (1 )for the total price , so the first equation becomes:

D + (1/16)D - 0.31 = 131.44

Now adding 0.31 to both sides we get:  

D + (1/16)D = 131.75

Since D is equivalent to (16/16)D we can substitute that for D and we get:

(16/16)D + (1/16)D = 131.75

= (17/16)D = 131.75

= 17D = 131.75*16

17D = 2108

D = 124

Hence, the cost of the desk is $124

So, Option D = $124.00 is correct