Name : ____________________ Date : _____________
Score : _____________
Write down your correct answer and show your workings:
1) There were 36 cars
and motorcycles in a car park.
Keith counted their wheels and found that there were a total of 104 wheels.
How many cars were
there?
2) Mrs Chan has more
than 50 sweets.
If she puts them in packets of 7, she has 5 sweets left.
If she puts them in packets of 9, she has 6 sweets left.
How many sweets does Mrs Chan have?
3) 3 similar files
and 2 similar books cost $60.
2 such files and 3 such books cost $70.
Find the cost of 1 file.
4) Ronaldo saw cars
and motor cycles in a car park.
He counted a total of 192 wheels and noted that there were 6 more motor
cycles than cars.
How many cars were there in the car park?
5) Some rectangular
tables and oval chairs are arranged as show below.
a) How many chairs are there in Figure 5?
b) How many tables are needed for 40 chairs?
Answers:
1) First, basic assumption is that a car has 4
wheels and a motorcycle has 2 wheels.
If all are motorcycles,
number of wheels= 36 x 2=72
Actual count = 104 wheels
Difference in the number
of wheels = 104 - 72 = 32
So, these 32 wheels came
from the extra 2 wheels from the cars.
32 / 2 = 16 (cars)
Therefore, number of cars
in the car park would be 16
2) As stated in the question, “Mrs Chan has more
than 50 sweets”.
So the exact number of
sweets she has is not known in the beginning.
Hence we use the “Multiples
Method”
Start with multiples of
7 and 9 which are greater than 50.
The common number after
listing in a tabulated form is the least number of sweets Mrs Chan has.
Number of Sweets
Multiples of 7
56 63 70 77
84 91 98
Multiples of 7 + 5
61 68 75 82
89 96 103
Multiples of 9
54 63 72 81
90 99
Multiples of 9 + 6
60 69 78 87
96 105
Mrs Chan has 96 sweets.
3) 3 files and 2 books cost $60 --------(1)
2 files and 3 books cost
$70 -------(2)
So:
5 files and 5 books cost
$130
1 file and 1 book cost
$26
2 files and 2 books cost
$52 -------(3)
From (1):
3 files and 2 books = 1
file + 2 files and 2 books
$60 = 1 file + $52
1 file = $8
The cost of 1file is $8
4) Cars: unit
Motor cycles: unit + 6
A car has 4 wheels and
1 motor cycle has 2 wheels (basic assumption for this question).
Number of wheels for the cars
= 4 x unit = 4 units
Number of wheels for the motorcycle
= 2 x (unit + 6) = 2 units + 12
Total = 192 wheels
4 units + 2 units + 12 = 192
6 units = 180
1 unit = 30
Therefore, number of cars in
the car park were 30
5) 1 table = 2 chairs + 2 chairs
Each Figure 1 increase
by 1 table.
Figure 5 will be (5 tables
x 2 chairs) + 2 chairs = 10 chairs + 2 chairs = 12 chairs.
a) Figure 5 will have
12 chairs
b) 2 chairs = 1 table + 2 chairs
40 chairs
= 40 - 2 = 38 chairs
38 /
2 = 19 tables