Question 1
1(a) Jason, Damien and Julia save their money in a ratio of 2:5:8
If Damien saves £45 a week, how much do they save in total?
ANSWER: Multiple Choice (Type 1)
A: \pounds 18
B: \pounds72
C: \pounds90
D: \pounds135
Answer: D
Workings:
\dfrac{45}{5} = 9
2 \times 9 =18
8 \times 9 = 72
Total = 18 + 45 + 72 = 135
Marks = 1
1(b) There are 37 horses in a field.
Alannah, David and Taylor are supposed to share the horses with a ratio of 4:2:1, with no part horses allowed.
What is the least number of horses that must be removed to allow this ratio to work with full numbers?
ANSWER: Simple text answer
Answer: 2
Workings:
4 + 2 + 1 = 7
37 = 35 + 2 = (5 \times 7) + 2
Marks = 1
1(c) The ratio used to share some money between two people is 3:5 One person gets \pounds16 less than another.
Express the amount each receives as a ratio.
ANSWER: Multiple Choice (Type 1)
A: 5:21
B: 19:35
C: 24:40
D: 48:64
Answer: C
Workings:
Ratio is 5:3 so difference = 2 parts
2 parts = 16
1 part = 8
3 \times 8 = 24
5 \times 8 = 40
So ratio is 24:40
Marks = 1
Question 2
The ratio of apples, a, to oranges, o, is 11 :17
Express this ratio as an equation in terms of a.
ANSWER: Multiple Choice (Type 2):
A: a= \dfrac{11}{17}o
B: a= \dfrac{17}{11}o
C: a= \dfrac{11}{28}o
D: a= \dfrac{28}{11}o
Answer: A
Workings:
\dfrac{a}{o} = \dfrac{11}{17}
a= \dfrac{11}{17}o
Marks = 2
Question 3
Given that,
x + 1 : 3y = 1:7, and 2x:y+3 = 2:5
Find x and y
ANSWER: Multiple answers (Type 1)
Answer: x = 2, y = 7
Workings:
\dfrac{x + 1}{3y} = \dfrac{1}{7} ; \dfrac{2x}{y + 3} = \dfrac{2}{5}
\dfrac{3y}{7}-1 = \dfrac{y + 3}{5} ; \dfrac{3y - 7}{7} = \dfrac{y + 3}{5}
15y - 35 = 7y + 21 ; 8y = 56 ; y = 7
\dfrac{2x}{7 + 3} = \dfrac{2}{5} ; 2x = \dfrac{20}{5} ; x = 2
Marks = 3
Question 4
A bag contains a mixture of 160 5p and 10p coins.
The ratio of 5p to 10p coins is 7:3
Some 10p coins are added so that now the ratio of 5p to 10p coins is 7:5
4(a) How many 10p coins were added?
ANSWER: Simple text answer
Answer: 32
Workings:
Ratio of 7:3 has 10 parts, each part has 16 coins.
7:3 = 112:48
7:5 = 112:80
Hence 32 10p coins have been added.
Marks = 3
4(b) What is the value of the coins before and after the additional 10p coins were added?
ANSWER: Multiple answers (Type 1)
Answer: 5p total = \pounds10.40, 10p total = \pounds13.60
Workings:
112 \times 5p = \pounds5.60 ; 48 \times 10p = \pounds4.80;
total is \pounds10.40
112 \times 5p = \pounds5.60 ; 80 \times 10p = \pounds8.00;
total is \pounds13.60
Question 5
In order to make a new colour, an artist combines 4 parts blue, 3 parts yellow and 7 parts red.
5(a) If the combination results in a quantity of 210 ml of paint, how much of each colour is used?
ANSWER: Multiple Answers (Type 1)
Answer: 60 ml blue; 45 ml yellow; 105 ml red.
Workings:
4:3:7 makes 14 parts,
each part is 15 ml
4 \times 15 ml = 60 ml
3 \times 15 ml = 45 ml
7 \times 15 ml = 105 ml
Marks = 3
5(b) The cost of blue paint is 6p per ml, yellow paint is 4p per ml and red paint is 2p per ml.
The mixture allows for 5 paintings to be created with only this colour.
Each painting sells for \pounds5.
How much profit does the artist make?
ANSWER: Simple text answer
Answer: \pounds17.50
Workings:
Blue paint 6p \times 60 = \pounds3.60;
Yellow paint 4p \times 45 = \pounds1.80;
Red paint 2p \times 105 =\pounds2.10
Total cost = \pounds7.50
5 \times \pounds5 = \pounds25
\pounds25 - \pounds7.50 = \pounds17.50
Marks = 3
Question 6
A survey is taken of students’ pets.
The results are expressed in the following ratios:
the number of cats to dogs is 3 : 2
the number of cats to birds is 4 : 1
6(a) If there were 207 animals recorded, how many birds were recorded?
ANSWER: Simple text answer
Answer: 27
Workings:
Let cats be c ;
Let dogs be \dfrac{2}{3} c ;
Let birds be \dfrac{1}{4} c
The ratio of cats to dogs to birds is 12:8:3, which has 23 parts
Number of birds = (\dfrac{207}{23} \times 3) = 27
Marks = 3
6(b) Find how many dogs were recorded.
ANSWER: Simple text answer
Answer: 72
Workings:
(\dfrac{207}{23} \times 8) = 72 dogs
Marks = 1
Question 7
At a children’s birthday party each child was given a party bag that was red, blue or green.
The ratio of red to blue party bags was 4:3
The ratio of blue to green was 3:2
Find the ratio of those who received a red party bag to those who received a green party bag.
ANSWER: Simple text answer
Answer: 2:1
Workings:
R : B : G = 4:3:2
So R : G = 4:2 = 2:1
Marks = 2
Question 8
A box contains a selection of red, blue and orange sweets in the ratio 4:3:6
6 blue sweets are added to the box making the probability of selecting a blue sweet \dfrac{1}{3}
8(a) What is the new total number of sweets in the box?
ANSWER: Simple text answer
Answer: 45
Workings:
From 4x:3x:6x, new ratio is 4x:3x+6:6x
Probability of blue sweet = \dfrac{3x + 6}{13x + 6} = \dfrac{1}{3}
9x + 18 = 13x + 6
4x = 12
x = 3
Total number of sweets = (4 \times 3) + (3 \times 3 + 6) + (6\times 3) = 45
Marks = 3
8(b) Hence what is the probability of randomly selecting an orange sweet?
ANSWER: Simple text answer
Answer: 0.4
Workings:
\dfrac{18}{45} = 0.4
Marks = 1
Question 9
A business has two different offices, one in London, the other in New York.
The ratio of the number of staff at the London office to New York office is 3 : 5
Employees of the business are either part time or full time.
In London 30\% of the staff are part time
In New York 20\% of the staff are part time
Given that the business has 38 part-time members of staff, work out the total number of employees.
ANSWER: Simple text answer
Answer: 160
Workings:
ratio of total employees is 3:5= 3x:5x
ratio of part time employees is (0.3 \times 3) : (0.2 \times 5) = 0.9x : x
total number of part time employees is 1.9x = 38
so, x = \dfrac{38}{1.9}, x = 20
Hence, 8 \times 20 = 160 employees
Marks = 3