This page focuses on using percentages within problem solving. Take a look at Fraction and percentage in order to recap percentages.

Dylan’s Deli reduces their sandwiches by 30% at 3pm. Calculate the cost of these sandwiches after 3pm:

• a ham sandwich, which originally cost £2.50
• a falafel sandwich, which cost £4

Ham sandwich

1. Find 30% of £2.50:

£2.50 ÷ 100 × 30 = £0.75

So there is a discount of 75p.

2. Subtract the discount from the original value:

£2.50 - £0.75 = £1.75

The discounted ham sandwich costs £1.75p.

Falafel sandwich

£4 ÷ 100 × 30 = £1.20

£4 - £1.20 = £2.80

The discounted falafel sandwich costs £2.80p.

You may notice that the falafel sandwich has a bigger discount. This is because the original price was higher.

There is an alternative way of calculating this. Sandwich prices are reduced by 30% which means that the reduced price is 70% of the original price.

Ham sandwich

70% of £2.50 = £2.50 ÷ 100 × 70 = £1.75

Falafel sandwich

70% of £4.00 = £4.00 ÷ 100 × 70 = £2.80

Question

Top TV has a £400 television on sale reduced by £80. Attic Appliances has the same TV originally priced at £350 with a 22% reduction. Who has reduced the TV by more and which TV is now cheaper?

ReductionSale price
Top TV£80£400 - £80 = £320
Attic Appliances£350 ÷ 100 × 22 = £77£350 - £77 = £273

Top TV reduced their TV by a larger amount but the TV is cheaper at Attic Appliances.

There is an alternative way of calculating the price at Attic Appliances.

The price is reduced by 22% which means that the reduced price is 78% of the original price.

78% of £350 = £350 ÷ 100 × 78 = £273