Solving Problems
Solving Problems
Level 7
1. Ratio
On this necklace the ratio of black beads to white beads is 1 : 3
[pic]
How many more black beads do you need to
add to make the ratio of black to white 3 : 1?
[pic] ................... black beads
1 mark
2. Ratio
(a) On this necklace the ratio of black beads to white beads is 1 : 3
[pic]
How many more black beads do you need to add to make the
ratio of black to white 3 : 1?
[pic] ................... black beads
1 mark
(b) Here is the necklace again.
[pic]
How many more black beads and white beads do you need to add to make the ratio of black to white 3 : 2?
[pic] ....................... 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.
[pic]
Another point, P, lies on the same horizontal line.
P is twice as far from A as it is from B.
What could the coordinates of point P be?
There are two possible answers. Give them both.
[pic]
(............., .............) or (............., .............)
2 marks
4. Red and blue cubes
In a bag, there are red and blue cubes in the ratio 4 : 7
[pic]
I add 10 more red cubes to the bag.
Now there are red and blue cubes in the ratio 6 : 7
[pic]
How many blue cubes are in the bag?
[pic]
...................
2 marks
5. Best buy
You can buy jars of the same jam in two sizes.
[pic]
454g for £1.59 340g for £1.25
Which jar is better value for money?
You must show working to explain your answer.
[pic]
Tick ([pic]) your answer.
[pic] [pic] A [pic] B
2 marks
6. Shadows
Tom’s height is 1.8m.
He stands near a tree.
[pic]
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?
[pic]
|m |
2 marks
7. Dissection
A square of area 64cm2 is cut to make two rectangles, A and B.
[pic]
The ratio of area A to area B is 3 : 1
Work out the dimensions of rectangles A and B.
[pic]
Rectangle A: ......................... cm by ......................... cm
Rectangle B: ......................... cm by ......................... cm
2 marks
8. Area A
The diagram shows a shaded rectangle.
It is divided into four smaller rectangles, labelled A, B, C and D.
[pic]
The ratio of area C to area B is 1 : 2
Calculate area A.
[pic]
........................ cm2
2 marks
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?
[pic]
...............................
2 marks
10. Juice
The table shows a recipe for a fruit drink.
|Type of juice |Amount |
|Orange |[pic]litre |
|Cranberry |[pic]litre |
|Grape |[pic]litre |
| |Total 1 litre |
I want to make 1[pic]litres of the same drink.
Complete the table below to show how much of each type of juice to use.
Show your working.
[pic]
|Type of juice |Amount |
|Orange |litre |
|Cranberry |litre |
|Grape |litre |
| |Total 1[pic] litres |
2 marks
11. Russian dolls
The heights of Russian dolls are in the ratio 4 : 6 : 7
[pic]
(a) In a set of dolls, the height of the middle doll is 9 cm.
What are the heights of the other dolls?
[pic]
...................... cm [pic] cm ...................... cm
smallest middle 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.
[pic]
...................... cm ...................... cm [pic] cm
smallest middle tallest
2 marks
12. Pictures
Here are four pictures, A, B, C and D. They are not to scale.
[pic]
(a) Picture A can be stretched horizontally to make picture B.
Show that the horizontal factor of enlargement is 1.5
[pic]
1 mark
(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?
[pic] ......................... cm
1 mark
13. Earnings
The table shows the average weekly earnings for men and women in 1956 and 1998.
|1956 |1998 |
|Men |£11.89 |£420.30 |
|Women |£6.16 |£303.70 |
(a) 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.
[pic]
........................... %
2 marks
(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.
[pic]
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.
[pic]
...............................
2 marks
................
................
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