A car costs £300. The price is then reduced by 20%. However, the shop increases the new price by 15%. Fadhila says, "20 - 15 = 5, so the original price of the car has been reduced 5%". Is she right? What is the final price of the car?

Fadhila is wrong. To work out price increases/decreases we need to multiply the original price by a decimal number. A reduce by 20% means multiplying by 0.8: we need to take away 20% of the original number. In decimal, 20% = 0.2, so we need to take away 0.2 * number. 1 - 0.2 = 0.8, which means that we are left with 0.8 * number after our calculation, hence we multiply by 0.8. To incresae the number, we add 15% of the number, which is the same as multiplying the new number by 1.15 (same argument). So to get our final number, we multiply by 0.8 * 1.15. 0.8 * 1.15 = 0.92. 1 - 0.92 is 0.08, so the new number is 8% reduced; we are left with 92% of the number, hence there is 8% missing so it has been reduced by 8%. This is not the 5% that Fadhila claimed.

The new price would be 300 * 0.8 * 1.15 (reducing by 20%, then increasing by 15%). 300 * 0.8 * 1.15 = 276. So the car is now worth £276.