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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