In January, Mary and Daniel had erasers in the ratio 5 : 3. In February, each of them gave away the same number of erasers. Mary then had four times as many erasers as Daniel.
- Find the ratio of the number of erasers Daniel had in January to the number of erasers he had in February.
- Find the ratio of the total number of erasers both had in January to the total number of erasers both had in February.
| |
Mary |
Daniel |
Difference |
| Before |
5x3 =
15 u |
3x3 =
9 u |
2x3 =
6 u |
| Change |
- 7 u |
- 7 u |
|
| After |
4x2 =
8 u |
1x2 =
2 u |
3x2 =
6 u |
(a)
Since Mary and Daniel gave away the same number of erasers, the difference in the number of erasers between Mary and Daniel at first and in the end remains the same.
Make the difference in the number of erasers at first and in the end the same. LCM of 2 and 3 is 6.
Daniel's erasers in January : Daniel's erasers in February
9 : 2
(b)
Total number of erasers in January
= 15 u + 9 u
= 24 u
Total number of erasers in February
= 8 u + 2 u
= 10 u
Total erasers in January : Total erasers in February
24 : 10
(÷2)12 : 5
Answer(s): (a) 9 : 2; (b) 12 : 5
