In May, Fanny and Sam had pens in the ratio 5 : 4. In June, each of them gave away the same number of pens. Fanny then had five times as many pens as Sam.
- Find the ratio of the number of pens Sam 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.
| |
Fanny |
Sam |
Difference |
| Before |
5x4 =
20 u |
4x4 =
16 u |
1x4 =
4 u |
| Change |
- 15 u |
- 15 u |
|
| After |
5x1 =
5 u |
1x1 =
1 u |
4x1 =
4 u |
(a)
Since Fanny and Sam gave away the same number of pens, the difference in the number of pens between Fanny and Sam 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 1 and 4 is 4.
Sam's pens in May : Sam's pens in June
16 : 1
(b)
Total number of pens in May
= 20 u + 16 u
= 36 u
Total number of pens in June
= 5 u + 1 u
= 6 u
Total pens in May : Total pens in June
36 : 6
(÷6)6 : 1
Answer(s): (a) 16 : 1; (b) 6 : 1
