In January, Esther and Zeph had cards in the ratio 3 : 2. In February, each of them gave away the same number of cards. Esther then had thrice as many cards as Zeph.
- Find the ratio of the number of cards Zeph had in January to the number of cards he had in February.
- Find the ratio of the total number of cards both had in January to the total number of cards both had in February.
| |
Esther |
Zeph |
Difference |
| Before |
3x2 =
6 u |
2x2 =
4 u |
1x2 =
2 u |
| Change |
- 3 u |
- 3 u |
|
| After |
3x1 =
3 u |
1x1 =
1 u |
2x1 =
2 u |
(a)
Since Esther and Zeph gave away the same number of cards, the difference in the number of cards between Esther and Zeph 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 1 and 2 is 2.
Zeph's cards in January : Zeph's cards in February
4 : 1
(b)
Total number of cards in January
= 6 u + 4 u
= 10 u
Total number of cards in February
= 3 u + 1 u
= 4 u
Total cards in January : Total cards in February
10 : 4
(÷2)5 : 2
Answer(s): (a) 4 : 1; (b) 5 : 2
