(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:

[tex]x = 0.25[/tex]

Step-by-step explanation:

Given

[tex]Cost\ Price = 6 + x[/tex]

[tex]Discount =8\%[/tex]

[tex]Amount\ Paid = R6 - x[/tex]

Required

Find x

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

This is calculated using:

[tex]Amount\ Paid = Cost\ Price * (100\% - Discount)[/tex]

[tex]Amount\ Paid = (6 + x) * (100\% - 8\%)[/tex]

[tex]Amount\ Paid = (6 + x) * 92\%[/tex]

Express as decimal

[tex]Amount\ Paid = (6 + x) * 0.92[/tex]

Open bracket

[tex]Amount\ Paid = 5.52 + 0.92x[/tex]

So, we have:

[tex]Amount\ Paid = 5.52 + 0.92x[/tex] and

[tex]Amount\ Paid = R6 - x[/tex] ---- given

Equate both

[tex]6 - x = 5.52 + 0.92x[/tex]

Collect like terms

[tex]- x -0.92x= 5.52-6[/tex]

[tex]-1.92x= -0.48[/tex]

[tex]1.92x= 0.48[/tex]

Solve for x

[tex]x = \frac{0.48}{1.92}[/tex]

[tex]x = 0.25[/tex]

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