A trader buys some oranges at #50 each. He finds that six of them are rotten. He sells the rest at #80 each and makes a profit of #450. How many oranges did he buy.

80(x-6) = 50x + 450

Where is the solving

Let's break down the information we have:

1. The trader buys some oranges at #50 each.
2. Six of the oranges are rotten.
3. The trader sells the rest of the oranges at #80 each.
4. The trader makes a profit of #450.

To find out how many oranges the trader bought, we need to work through the problem step by step.

Step 1: Calculate the cost of the six rotten oranges
As the trader bought each orange at #50, the cost of six rotten oranges is 6 * #50 = #300.

Step 2: Calculate the profit made from selling the remaining oranges
We know that the trader made a profit of #450, so this amount represents the difference between the selling price and the cost price of the remaining oranges. Let's assume the trader bought x oranges initially.

The selling price of the remaining oranges is (#80 * (x - 6)).
The cost price of the remaining oranges is (#50 * (x - 6)).

So, we can create an equation to represent the profit: (#80 * (x - 6)) - (#50 * (x - 6)) = #450.

Step 3: Solve the equation
Let's simplify the equation:
#80x - #480 - #50x + #300 = #450,
#30x - #180 = #450,
#30x = #450 + #180,
#30x = #630.

Dividing both sides of the equation by #30 gives x = #630 / #30 = 21.

Step 4: Determine the number of oranges bought
The trader bought x oranges, which we calculated to be 21.

Therefore, the trader bought 21 oranges in total.