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)
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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.
