SOLUTION: Charlene paid $131.44, including tax, for a desk. The tax was 31 cents less than 1/16 the cost of the desk. Find the cost of the desk. If anyone can answer this question

Question 117365This question is from textbook Algebra Structure and Method
: Charlene paid $131.44, including tax, for a desk. The tax was 31 cents less than 1/16 the cost of the desk. Find the cost of the desk.

If anyone can answer this question I would appreciate it very much. Please and Thank You This question is from textbook Algebra Structure and Method

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Start by letting D represent the cost of the desk and T represent the tax paid.
.
The first sentence tells you that the cost of the desk plus the tax equals $131.44. In
equation form this is:
.
D + T = 131.44
.
The second sentence tells you that the tax T equals (1/16) times the cost of the desk less 0.31 dollars.
In equation form this is
.
T = (1/16)D - 0.31
.
Substitute the right side of this equation for T into the first equation for the total price
and the first equation becomes:
.
D + (1/16)D - 0.31 = 131.44
.
Get rid of the -0.31 on the left side by adding 0.31 to both sides to get:
.
D + (1/16)D = 131.75
.
Since D is equivalent to (16/16)D you can substitute that for D and you get:
.
(16/16)D + (1/16)D = 131.75
.
The sum of the two terms on the left side is:
.
(17/16)D = 131.76
.
You can solve this equation for D by either dividing both sides by (17/16) or by multiplying
both sides by (16/17). In either case you get:
.
D = (16/17)*131.75 = (16*131.75)/17
.
Calculator time. 16 times 131.75 = 2108 and dividing that product by 17 gives and answer of:
.
D = $124.
.
That's the answer. The cost of the desk was $124.00
.
Hope this helps you to understand the problem.

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