In February, Roshel and Michael had cards in the ratio 9 : 5. In March, each of them gave away the same number of cards. Roshel then had thrice as many cards as Michael.
- Find the ratio of the number of cards Michael had in February to the number of cards he had in March.
- Find the ratio of the total number of cards both had in February to the total number of cards both had in March.
| |
Roshel |
Michael |
Difference |
| Before |
9x1 =
9 u |
5x1 =
5 u |
4x1 =
4 u |
| Change |
- 3 u |
- 3 u |
|
| After |
3x2 =
6 u |
1x2 =
2 u |
2x2 =
4 u |
(a)
Since Roshel and Michael gave away the same number of cards, the difference in the number of cards between Roshel and Michael at first and in the end remains the same.
Make the difference in the number of cards at first and in the end the same. LCM of 4 and 2 is 4.
Michael's cards in February : Michael's cards in March
5 : 2
(b)
Total number of cards in February
= 9 u + 5 u
= 14 u
Total number of cards in March
= 6 u + 2 u
= 8 u
Total cards in February : Total cards in March
14 : 8
(÷2)7 : 4
Answer(s): (a) 5 : 2; (b) 7 : 4
