A trader bought two items of a total of R600. He sold one of them and realised a mark-up of 22% and from the other he realised a mark-up of 8%,and made no loss or profit in the end. Calculate the selling prices of the two items. [marks 9]

x+y = 600

1.22x + 1.08y = 600

250 To calculate the selling prices of the two items, we first need to determine their original prices.

Let's assume the original price of the item with a 22% markup is P1, and the original price of the item with an 8% markup is P2.

We know that the trader bought both items for a total of R600. Therefore, we can set up the following equation:

P1 + P2 = R600 (equation 1)

The trader sold one item with a 22% markup. This means that the selling price of that item will be the original price (P1) plus a 22% increase. Mathematically, this can be expressed as:

Selling Price 1 = P1 + 0.22P1 = 1.22P1 (equation 2)

The trader also sold the second item with an 8% markup. The selling price of this item is calculated similarly:

Selling Price 2 = P2 + 0.08P2 = 1.08P2 (equation 3)

The problem states that the trader made no loss or profit in the end. This means that the total selling price of both items should equal the total cost price of both items:

Selling Price 1 + Selling Price 2 = P1 + P2 = R600 (equation 4)

We now have four equations that can be solved simultaneously to find the values of P1 and P2.

Solving equations 1 and 4 together, we get:

P1 = 600 - P2 (equation 5)

Substituting equation 5 into equation 2, we get:

Selling Price 1 = 1.22(600 - P2) = 732 - 1.22P2 (equation 6)

Substituting equation 5 into equation 3, we get:

Selling Price 2 = 1.08P2 (equation 7)

Now we have equations 6 and 7, which represent the selling prices of both items. By substituting these values back into the original equations, we can solve for P1 and P2.

To calculate the selling prices of the two items, you can substitute the values of P1 and P2 into equations 6 and 7, respectively.

I hope this helps you understand how to approach and solve the problem.