Dipen and Nisha are planning their wedding reception. Nisha says, “I want to invite 70 guests.” Dipen says, “If we invite one-fifth fewer guests, we will save more than £500” Is Dipen correct? (Taken from Nov 2014 AQA Unit 2)

Need to calculate two things in order to answer the question:

1) Total cost of Nisha's 70 guests.

2) Total cost of Dipen's 'one-fifth fewer' guests.

For Nishen: Total cost = £40 * 70 minus the 5% reduction

= £2800 minus 5%

To work out 5% you divide by 20

2800/20 = 280/2 = 140

£2800 - 140 = £2660

For Dipen:

Work out how many guests is 'one-fifth fewer'

To calcuate a fifth, divide by five.

70/5 = 14

70 - 14 = 56

So Dipen wants to invite 56 people, which doesn't qualify for the 5% reduction.

So his total is £40 * 56

Which we can split into (£40 * 50) + (£40 * 6)

= (2000) + (240)

= 2240

Dipen is right that his number of guests is cheaper, but we need to calculate if it is £500 cheaper.

Nisha's £2660 - Dipen's £2240 = £420

420 < 500 so the answer is No, Dipen is in fact wrong.