02. Ratio 6-9

Question 1

LEVEL 4

In a necklace of 104 beads, there are red to blue beads in the ratio of 5:8.

How many red beads does the necklace have?

Select the correct answer from the list below:

A: 40

B: 21

C: 65

D: 36

CORRECT ANSWER:   A: 40

WORKED SOLUTION:

Add the separate ratio values together i.e. 5+8=13

Divide 104  by the answer i.e. 104\div13=8

Multiply the ratio  5:8 by 8, to get 40:64

Hence, in a necklace of 104 beads, where the ratio of red to blue is 5:8, there are 40 red beads.

Question 2

LEVEL 4

Share \pounds56 between Tom and Sarah in the ratio 3 : 4.

Select the correct answer from the list below:

A: 168:224

B: 56:75

C: 24:32

D: 24:56

CORRECT ANSWER:  C: 24:32

WORKED SOLUTION:

Add the separate ratio values together i.e. 3+4=7

Divide 56  by the answer i.e. 56\div7=8

Multiply the ratio  3:4 by 8

Hence \pounds 56 shared between Tom and Sarah in the ratio 3 :4 is 24 :32

Question 3

LEVEL 4

Divide 154 in the ratio \frac{3}{4} : \frac{1}{5} : \frac{1}{3}.

Select the correct answer from the list below:

A: 90:20:40

B: 100:29:25

C: 100:24:30

D: 90:24:40

CORRECT ANSWER:  D: 90 : 24 : 40

WORKED SOLUTION:

Firstly will need to add each term from the ratio together so, \frac{3}{4} + \frac{1}{5} +\frac{1}{3}= \frac{77}{60}

Then divide 154 by that total.

Final we will multiply each term by 120 to find the ratio, \frac{3}{4}\times120= 90,  \frac{1}{5}\times120= 24,\frac{1}{3}\times120= 40 ,

Therefore the ratio is 90 : 24 : 40

Question 4

LEVEL 4

Harry, Barry and Garry share some marbles in the ratio 1:2:5.

Harry has 12 marbles less than Garry. How many marbles does Barry have?

Select the correct answer from the list below:

A: 3

B: 4

C: 6

D: 8

CORRECT ANSWER:    C: 6

WORKED SOLUTION:

Firstly, we need to calculate how many parts of the ratio 12 marbles makes up:

Then divide to find 1 part:

12 \text{ marbles} \div 4 = 3 \text{ marbles}

3 \text{ marbles} = 1 \text{ part}

Finally, multiply by the number of parts Barry has to find how many marbles he has:

Question 5

LEVEL 4

Virgil and Leroy share chocolate blocks in the ratio 4:3. Virgil gives 6 blocks to Leroy, and the ratio is now 5:9.

How many blocks did Virgil have initially?

Select the correct answer from the list below:

A: 8

B: 12

C: 15

D: 16

CORRECT ANSWER:    D: 16

WORKED SOLUTION:

At first, Virgil had 4x blocks and Leroy had 3x blocks.

Virgil gives 6 blocks to Leroy. Now Virgil has 4x - 6 blocks and Leroy has 3x+6.

The ratio 4x-6:3x+6 is equal to 5:9.

\dfrac{4x-6}{3x+6} = \dfrac{5}{9}

9(4x-6) = 5(3x+6)

36x - 54 = 15x + 30

21x = 84

x = 4

Initially, Virgil had 4x = 16 blocks of chocolate.

Question 6

LEVEL 4

Reduce the ratio 4:21 to the form 1:n.

Select the correct answer from the list below:

A: 1:5

B: 1:5.25

C: 1:5.5

D: 1:5.75

CORRECT ANSWER:       B: 1:5.25

WORKED SOLUTION:

Divide both sides of the ratio by 4, to get