In May, Gillian and Luke had stamps in the ratio 13 : 10. In June, each of them gave away the same number of stamps. Gillian then had thrice as many stamps as Luke.
- Find the ratio of the number of stamps Luke had in May to the number of stamps he had in June.
- Find the ratio of the total number of stamps both had in May to the total number of stamps both had in June.
| |
Gillian |
Luke |
Difference |
| Before |
13x2 =
26 u |
10x2 =
20 u |
3x2 =
6 u |
| Change |
- 17 u |
- 17 u |
|
| After |
3x3 =
9 u |
1x3 =
3 u |
2x3 =
6 u |
(a)
Since Gillian and Luke gave away the same number of stamps, the difference in the number of stamps between Gillian and Luke at first and in the end remains the same.
Make the difference in the number of stamps at first and in the end the same. LCM of 3 and 2 is 6.
Luke's stamps in May : Luke's stamps in June
20 : 3
(b)
Total number of stamps in May
= 26 u + 20 u
= 46 u
Total number of stamps in June
= 9 u + 3 u
= 12 u
Total stamps in May : Total stamps in June
46 : 12
(÷2)23 : 6
Answer(s): (a) 20 : 3; (b) 23 : 6
