Ratio P6 2009 SA2 P2 Rulang Q8

8. Maggie had a total of 120 red and blue pens in the ratio 3 : 5. After she had given away an equal number of each type of pens, the number of red and blue pens left was in the ratio 3 : 8. How many pens did she give away altogether?

The differences in the number of red and blue pens before and after are the same – Constant Difference. So we need to make the differences in the two given ratios the same (by multiply them by the respective difference of the other ratio).

3 : 5 = 15 : 25

3 : 8 = 6 : 16

Total number of units (15 + 25). If you like you may show how you get 40.

40 u -- > 120

1 u -- > 120 ÷ 40 = 3

Units given away is (15 - 6) and (25 – 16). So total number is 18 units. Again if you like you may show how you get 18.

18 u -- > 9 x 3 = 54 pens

She gave away 54 pens altogether.

Ratio P6 2009 SA2 P2 Rulang Q17

17. For every $2 that Eddy spent, Fred spent $3. After Eddy had spent all his money, Fred still had 3/8 of the total amount of money the two boys had at first.

a) What fraction of the total amount of money did Eddy have at first?

b) What was the ratio of Fred’s money to Eddy’s money at first?

E [S][S]

F [S][S][S][ ][ ][ ]

2/8 = 1/4

a) Eddy had 1/4 of the total money at first.

6 : 2 = 3 : 1

b) The ratio of Fred’s money to Eddy’s money at first was 3 : 1.

Ratio P6 2009 SA2 P2 Rulang Q18

18. Mrs Oon used sugar, vinegar and chillies to make chilli sauce. The mass of sugar to that of vinegar to that of chillies used was in the ratio 5 : 1 : 2. The cost of the ingredients was as follows:

If Mrs Oon spent $9.15 on the ingredients, what was the total mass of the ingredients used?

5 x 0.72 = 3.60

1 x 0.90 = 0.90

2 x 0.80 = 1.50

3.60 + 0.90 + 1.50 = 6.10

9.15 ÷ 6.10 = 1.5

5 + 1 + 2 = 8

8 x 100 = 800

800 x 1.5 = 1200 g

The mass of the ingredients was 1200 g.