In May, Yen and Liam had pens in the ratio 5 : 2. In June, each of them gave away the same number of pens. Yen then had five times as many pens as Liam.
- Find the ratio of the number of pens Liam had in May to the number of pens he had in June.
- Find the ratio of the total number of pens both had in May to the total number of pens both had in June.
| |
Yen |
Liam |
Difference |
| Before |
5x4 =
20 u |
2x4 =
8 u |
3x4 =
12 u |
| Change |
- 5 u |
- 5 u |
|
| After |
5x3 =
15 u |
1x3 =
3 u |
4x3 =
12 u |
(a)
Since Yen and Liam gave away the same number of pens, the difference in the number of pens between Yen and Liam at first and in the end remains the same.
Make the difference in the number of pens at first and in the end the same. LCM of 3 and 4 is 12.
Liam's pens in May : Liam's pens in June
8 : 3
(b)
Total number of pens in May
= 20 u + 8 u
= 28 u
Total number of pens in June
= 15 u + 3 u
= 18 u
Total pens in May : Total pens in June
28 : 18
(÷2)14 : 9
Answer(s): (a) 8 : 3; (b) 14 : 9
