The price of a washing machine is reduced by 20% for a sale. Afterwards, the sale price is increased by 30%.

Joachim says

The washing machine is now 10% more expensive than before the sale.

Explain Joachim’s error and work out the correct percentage change in the price of the washing machine from before the sale to after the sale

1) Joachim's error is in applying the 30% increase to the initial price of the washing machine, 'x', rather than the reduced price of the washing machine for the sale, which is 0.8·x

2) The correct percentage change in price is 4%

Step-by-step explanation:

The price of the washing machine has the following parameters;

The percentage reduction of the price of the washing machine for a sale = 20%

The percentage by which the price is increased afterwards = 30%

Let 'x' represent the initial selling price of the washing machine before the price decrease, and let 'P' represent the sale price after the price increase, we have;

The price after the 20% reduction = x - 20% × x = x - (20/100) × x = 0.8·x

The price after the 30% increase after the sale = 0.8·x + 30% × 0.8·x = 0.8·x + 30/100 × 0.8×x = 0.8·x + 0.3 × 0.8·x = 1.04·x = x + 0.04·x = x + (4/100) × x = x + 4% × x

Therefore, Joachim's error is in applying the 30% increase to the initial price of the washing machine, 'x', rather than the reduced price of the washing machine for the sale, which is 0.8·x

2) The percentage change in the price after the sale is given as follows;

Price of the washing machine after the sale, P = 1.04·x = (104/100) × x = 104% × x

∴ P = 100%x + 4%x = (100/100)·x + 4%x = x + 4%

The percentage change in price = P - x = x + 4% - x = 4%

The correct percentage change in price = 4%