4 Multistage calculations
Often in daily life you will come across problems that require more than one calculation to reach the final answer.
Example: Multistage calculations
Four friends are planning a holiday. The table below shows the costs:
| Item | Price |
|---|---|
| Flight (return) | £305 per person |
| Taxes | £60 per person |
| Hotel | £500 per room. 2 people per room |
| Taxi to airport | £45 |
The friends will be sharing the total cost equally between them. How much do they each pay?
Method
First we use multiplication to find the cost of items that we need more than one of:
Flights = £305 × 4 = £1220
Taxes = £60 × 4 = £240
Hotel = 2 rooms required for 4 people = £500 × 2 = £1000
Now we use addition to add these totals together along with the taxi fare:
£1220 + £240 + £1000 + £45 = £2505
Finally, we need to use division to find out how much each person pays:
£2505 ÷ 4 =£626.25 each
Activity 10: Multistage calculations
Your current mobile phone contract costs you £24.50 per month.
You are considering changing to a new provider. This provider charges £19.80 per month along with an additional, one off connection fee of £30.
How much will you save over the year by switching to the new provider?
You are going on holiday and you have decided to stay in a cottage in North Wales for 7 nights.
There will be 12 of you staying and the total cost of the cottage you have chosen is £460 per night. If you split the cost equally, how much will each of you pay?
Answer
First calculate the cost with the current provider
monthly cost × 12
£24.50 × 12 = £294 (current provider)
Second, calculate the cost of the new provider.
To do this you need to calculate the total monthly costs:
£19.80 × 12 = £237.60
and then add on the one off connection fee of £30:
£237.60 + £30 = £267.60 (new provider)
Finally you can calculate the difference between the two providers:
£294 − £267.60 = £26.40 saved
To do your calculation, you need to work out the cost for 7 nights. Once you have done this, you can divide the total by 12:
460 × 7 = £3220
£3220 ÷ 12 = £268.33 (rounded to two d.p.)
Here we would probably round this amount up to £268.34 per person to make sure the full cost is covered.
All the examples we have looked at until now have used positive numbers. However, as anyone with an overdraft will know, numbers (or bank balances) are not always positive! Our next section therefore deals with negative numbers.
Summary
In this section you have:
applied the four operations to solve multistage calculations.