Solving Problems
Level 7
1.
Ratio
On this necklace the ratio of black beads to white beads is 1 : 3
How many more black beads do you need to
add to make the ratio of black to white 3 : 1?
................... black beads
1 mark
2.
Ratio
(a)
On this necklace the ratio of black beads to white beads is 1 : 3
How many more black beads do you need to add to make the
ratio of black to white 3 : 1?
................... black beads
1 mark
Brewood CE C Middle School
1
(b)
Here is the necklace again.
How many more black beads and white beads do you need to add to make the
ratio of black to white 3 : 2?
....................... black beads, ....................... white beads
1 mark
3.
Twice as far
Point A has coordinates (4, 3) and point B has coordinates (10, 3)
They lie on a horizontal line.
6
4
A
B
2
–2
0
2
4
6
8
10
12
14
16
Another point, P, lies on the same horizontal line.
P is twice as far from A as it is from B.
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2
What could the coordinates of point P be?
There are two possible answers. Give them both.
(............., .............) or (............., .............)
2 marks
4.
Red and blue cubes
In a bag, there are red and blue cubes in the ratio 4 : 7
red : blue
4:7
I add 10 more red cubes to the bag.
Now there are red and blue cubes in the ratio 6 : 7
red : blue
6:7
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3
How many blue cubes are in the bag?
...................
2 marks
5.
Best buy
You can buy jars of the same jam in two sizes.
454g for £1.59
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340g for £1.25
4
Which jar is better value for money?
You must show working to explain your answer.
Tick ( ) your answer.
A
B
2 marks
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5
6.
Shadows
Tom’s height is 1.8m.
He stands near a tree.
Height
of tree
1.8m
2.7m
6.3m
Not drawn accurately
At 4pm, the length of Tom’s shadow is 2.7m.
At 4pm, the length of the tree’s shadow is 6.3m.
What is the height of the tree?
m
2 marks
Brewood CE C Middle School
6
7.
Dissection
A square of area 64cm2 is cut to make two rectangles, A and B.
A
B
Area = 64 cm 2
Not drawn
accurately
The ratio of area A to area B is 3 : 1
Work out the dimensions of rectangles A and B.
Rectangle A: ......................... cm by ......................... cm
Rectangle B: ......................... cm by ......................... cm
2 marks
Brewood CE C Middle School
7
8.
Area A
The diagram shows a shaded rectangle.
It is divided into four smaller rectangles, labelled A, B, C and D.
5 cm
3 cm
A
C
5 cm
B
D
Not drawn
accurately
10 cm
The ratio of area C to area B is 1 : 2
Calculate area A.
........................ cm2
2 marks
Brewood CE C Middle School
8
9.
Rich and poor
A newspaper printed this information about the world’s population.
If the world was a village of 100 people,
6 people would have 59% of the total wealth.
The other 94 people would have the rest.
On average, how many times as wealthy as one of the other 94 people would one
of these 6 people be?
...............................
2 marks
Brewood CE C Middle School
9
10.
Juice
The table shows a recipe for a fruit drink.
Type of juice
Amount
Orange
1 litre
2
Cranberry
1 litre
3
Grape
1 litre
6
Total 1 litre
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10
I want to make 1 1 litres of the same drink.
2
Complete the table below to show how much of each type of juice to use.
Show your working.
Type of juice
Amount
Orange
litre
Cranberry
litre
Grape
litre
Total 1 1 litres
2
2 marks
11.
Russian dolls
The heights of Russian dolls are in the ratio 4 : 6 : 7
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11
(a)
In a set of dolls, the height of the middle doll is 9 cm.
What are the heights of the other dolls?
...................... cm
smallest
9
............................
cm
middle
...................... cm
tallest
1 mark
(b)
In another set of dolls, the height of the tallest doll is 9 cm.
What are the heights of the other dolls?
Show your working, and give your answers to 1 decimal place.
...................... cm
smallest
...................... cm
middle
9
............................
cm
tallest
2 marks
Brewood CE C Middle School
12
12.
Pictures
Here are four pictures, A, B, C and D. They are not to scale.
4 cm
6 cm
A
B
5.6 cm
5.6 cm
C
D
h cm
h cm
4 cm
(a)
6 cm
Picture A can be stretched horizontally to make picture B.
Show that the horizontal factor of enlargement is 1.5
1 mark
Brewood CE C Middle School
13
(b)
Picture A can be stretched vertically to make picture C.
The vertical factor of enlargement is 1.25
What is the height, h, of picture C?
......................... cm
1 mark
13.
Earnings
The table shows the average weekly earnings for men and women in 1956 and 1998.
(a)
1956
1998
Men
£11.89
£420.30
Women
£6.16
£303.70
For 1956, calculate the average weekly earnings for women as a percentage of
the average weekly earnings for men.
Show your working and give your answer to 1 decimal place.
........................... %
2 marks
Brewood CE C Middle School
14
(b)
For 1998, show that the average weekly earnings for women were a greater
proportion of the average weekly earnings for men than they were in 1956.
2 marks
14.
Centenarians
People who live to be 100 years old are called centenarians.
In 1998 there were 135 000 centenarians.
The ratio of male to female was 1 : 4
How many female centenarians were there in 1998?
Show your working.
...............................
2 marks
Brewood CE C Middle School
15