In March, Gem and Howard had cards in the ratio 11 : 5. In April, each of them gave away the same number of cards. Gem then had four times as many cards as Howard.
- Find the ratio of the number of cards Howard had in March to the number of cards he had in April.
- Find the ratio of the total number of cards both had in March to the total number of cards both had in April.
| |
Gem |
Howard |
Difference |
| Before |
11x1 =
11 u |
5x1 =
5 u |
6x1 =
6 u |
| Change |
- 3 u |
- 3 u |
|
| After |
4x2 =
8 u |
1x2 =
2 u |
3x2 =
6 u |
(a)
Since Gem and Howard gave away the same number of cards, the difference in the number of cards between Gem and Howard 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 6 and 3 is 6.
Howard's cards in March : Howard's cards in April
5 : 2
(b)
Total number of cards in March
= 11 u + 5 u
= 16 u
Total number of cards in April
= 8 u + 2 u
= 10 u
Total cards in March : Total cards in April
16 : 10
(÷2)8 : 5
Answer(s): (a) 5 : 2; (b) 8 : 5
