Question

A store offers a discount of 30% on a game. There is a sales tax of 6%. If "T" is the total price with tax, then T(x) = 1.06 x. If "D" is the price after discount, then D(x) = 0.70 x. Which of the following represents the discount being taken before the sales tax is applied?

A) D(T(x))
B) T(x) / D(x)
C) T(x)
D) D(x)
E) D(x) / T(x)
F) T(D(x))

Answer 1

The correct option would be F) T(D(x))

Explanation:

Suppose x represents the original price of the game,

After getting 30% discount,

New price of game = x - 30% of x

`=x -(30x)/(100)`

= x - 0.30x

= 0.70x

Now, if there is a tax of 6%,

Then the final price of the game = 0.70x + 6% of 0.70x

`=0.70x +(6* 0.70x)/(100)`

= 0.70x + 0.06(0.70x)

= (1+0.06)(0.70x)

= 1.06(0.70x)

= T(0.70x) ( ∵ T(x) = 1.06x )

= T(D(x)) ( ∵ D(x) = 0.70x )

Hence, OPTION F represents the discount being taken before the sales tax is applied.