In January, Sarah and Michael had pens in the ratio 13 : 4. In February, each of them gave away the same number of pens. Sarah then had five times as many pens as Michael.
- Find the ratio of the number of pens Michael had in January to the number of pens he had in February.
- Find the ratio of the total number of pens both had in January to the total number of pens both had in February.
| |
Sarah |
Michael |
Difference |
| Before |
13x4 =
52 u |
4x4 =
16 u |
9x4 =
36 u |
| Change |
- 7 u |
- 7 u |
|
| After |
5x9 =
45 u |
1x9 =
9 u |
4x9 =
36 u |
(a)
Since Sarah and Michael gave away the same number of pens, the difference in the number of pens between Sarah and Michael 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 9 and 4 is 36.
Michael's pens in January : Michael's pens in February
16 : 9
(b)
Total number of pens in January
= 52 u + 16 u
= 68 u
Total number of pens in February
= 45 u + 9 u
= 54 u
Total pens in January : Total pens in February
68 : 54
(÷2)34 : 27
Answer(s): (a) 16 : 9; (b) 34 : 27
