Question

(i) Challenge: Thembi received 8% discount on an item which cost

R6 plus x cents. The price she paid was R6 minus x cents.
Determine the value of x.

Answer 1

`x = 0.25`

Explanation:

Given

`Cost\ Price = 6 + x`

`Discount =8\%`

`Amount\ Paid = R6 - x`

Required

Find x

First, we calculate the amount paid in terms of the cost price.

This is calculated using:

`Amount\ Paid = Cost\ Price * (100\% - Discount)`

`Amount\ Paid = (6 + x) * (100\% - 8\%)`

`Amount\ Paid = (6 + x) * 92\%`

Express as decimal

`Amount\ Paid = (6 + x) * 0.92`

Open bracket

`Amount\ Paid = 5.52 + 0.92x`

So, we have:

`Amount\ Paid = 5.52 + 0.92x` and

`Amount\ Paid = R6 - x` ---- given

Equate both

`6 - x = 5.52 + 0.92x`

Collect like terms

`- x -0.92x= 5.52-6`

`-1.92x= -0.48`

`1.92x= 0.48`

Solve for x

`x = (0.48)/(1.92)`

`x = 0.25`