﻿ Unit 2 Section 4 : Problems in Context

# Unit 2 Section 4 : Problems in Context

Problems in context are dealt with in this section. You will need to decide which operation is required to solve each problem: you may need to add, subtract, multiply or divide. However, it is still recommended that you tackle these problems without a calculator, perhaps using it only to check your answers.

## Example 1

It costs £1.25 for a child to go into a swimming pool. How much does it cost for 7 children to go in?

## Example 2

There are 242 passengers on a train. At a station, 36 people get off and 27 people board the train. How many people are now on the train?

## Example 3

Four children want to buy a computer game that costs £24.80. How much money must each of them contribute if they share the cost equally between them?

## Exercises

Work out the answers to the questions below and fill in the boxes. Click on the button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on to see the answer.
Question 1
A blank tape costs 65p. Calculate the cost of:
 (a) 4 tapes £ (b) 7 tapes £ (c) 9 tapes £
Question 2
Alec spends £14.27 in a shop. He pays with a £20 note. How much change should he get?
£
Question 3
The cost of a carpet is £7.99 per square metre. Calculate the cost of:
 (a) 4 square metres £ (b) 10 square metres £ (c) 9 square metres £
Question 4
Simon is saving up to buy a tent that costs £72. So far he has saved £54.50.
How much more does he need to save?
£
Question 5
Two neighbours agree to share equally the cost of a new fence. The fence costs £142.
How much do they each have to pay?
£
Question 6
A cake weighs 824 grams. It is divided into 4 equal parts.
How much does each part weigh?
grams
Question 7
A car is driven at a speed of 45 mph. How far does it travel in:
 (a) 2 hours miles (b) 5 hours miles (c) 3.5 hours miles
Question 8
Cinema tickets cost £7 each. How many tickets could you buy with £63 ?
tickets
Question 9
Cans of drink cost 42p each.
 (a) How much would 6 cans cost? £ (b) Jane's mum pays for 6 cans with a £5 note. How much change should she have? £
Question 10
A school trip is arranged for 43 pupils accompanied by 2 teachers. A minibus carries 16 passengers. Three minibuses are booked for the trip.
How many empty seats are there in the minibuses?
empty seats
Question 11

(a) A shop sells plants at 95p each. Find the cost of 35 plants.

£

(b) The shop also sells trees at £17 each. Mr Bailey has £250. He wants to buy as many trees as possible.
How many trees can Mr Bailey buy?

trees

Question 12

(a) Lucy had dinner. It cost £13.40. She paid with a £20 note.
How much change should Lucy get?

£

(b)

(i) 14 people had the set meal at the cafe at a cost of £6.40 each.
How much did they pay altogether?

£

(ii) Another group of people had the set meal. Altogether they paid £32.
How many people were in the group?

people

Question 13
Five people shared a bag of apples.
Each person had the same number of apples.
There were none left.

(a) How many apples could have been in the bag?

(b) Write another number of apples which could have been in the bag.

(c) Write another number of apples which could have been in the bag.

The five people shared a box of sweets.
There were more than 100 sweets in the box.
Each person had the same number of sweets.
There were none left.

(d) Anna says: "I think there were 113 sweets in the box." Is Anna right?

Anna is wrong because 113 is not a multiple of 5,
since 113 ÷ 5 = 22 remainder 3.

(e) Write two different numbers of sweets which could have been in the box.

and

(f) How can anyone tell that your numbers could be divided by 5 just by looking at how they end?

They can be divided by 5 because the last digit is either.
Question 14
(a)
Carl is putting packs of biscuits into a box.
He starts to put in the bottom layer.
The box holds 5 packs across and is 4 packs wide.

How many packs will fit altogether on the bottom layer?

packs

The box holds 6 layers.

How many packs will fit in the box when it is full?

packs

(b)
Aziz is putting packs of tea into a box.
The box holds 5 packs across and is 6 packs wide.
The box holds 3 layers.

How many packs of tea will fit in the box when it is full?

packs of tea

(c)
Fill in the gaps to show one way of filling a different box with 24 packs in 2 layers.

 total: 24 packs 2 layers packs across packs wide
Question 15

(a) A shop sells video tapes for £2.50 each.
What is the cost of 16 video tapes?

£

(b) The shop sells audio cassettes. Each cassette costs £1.49.
What is the cost of 4 cassettes?

£

(c) How many cassettes can you buy with £12?

casettes

(d) The shop also sells cassettes in packs of three. A pack costs £3.99.
How many packs can you buy with £12?

packs

(e) What is the greatest number of cassettes you can buy with £15? You can buy some packs and some single cassettes.

casettes
Question 16
Bill, Ravi and Eric are three divers in a competition. Each type of dive has a dive rating.
Easy dives have a low rating; hard dives have a high rating.

Every dive is marked by five judges who each give a mark out of 10.

How to calculate the score for a dive:

1. Look at all five marks. Remove the highest and the lowest marks.
2. Add together the middle three marks to give a total.
3. Multiply this total by the dive rating.

(a) Bill does a dive with a dive rating of 3.34.
The judges give the marks 7.0 7.5 8 .0 8.0 8.5
What is Bill's score?

(b) Ravi scored 82.68 on his first dive.
The dive had a dive rating of 3.18.
What was the total of the middle three marks given by the judges?

(c) Eric is getting ready to take his final dive.
He needs to score at least 102.69 to win the competition.
Eric decides to do a dive with a dive rating of 3.26.
Has Eric made a good decision?

102.69 ÷ 3.26 = 31.5, which means that he must get a total of 31.5 from his middle three marks. The highest he can get is 3 × 10 = 30, so 31.5 is impossible, i.e. he cannot win with this dive.
Question 17
A class is planning a trip to a funfair.
The pupils have found out the prices at these two funfairs:
Milltown Funfair
Entry: £2.20
plus
Rides: 60p each
Seaview Funfair
Entry: £4.50
plus
Rides: 20p each
The teacher says that there will be time for 8 rides.

(a) How much money do you need to get in to Milldown Funfair and have 8 rides?

£

(b) How much money do you need to get in to Seaview Funfair and have 8 rides?

£

Ben has only £5 to get in and pay for his rides.

(c) How many rides would Ben get at each funfair?

At Milltown Funfair, Ben would getrides.
At Seaview Funfair, Ben would getrides.