In May, Hilda and Jenson had cards in the ratio 13 : 7. In June, each of them gave away the same number of cards. Hilda then had five times as many cards as Jenson.
- Find the ratio of the number of cards Jenson had in May to the number of cards he had in June.
- Find the ratio of the total number of cards both had in May to the total number of cards both had in June.
|
Hilda |
Jenson |
Difference |
Before |
13x2 = 26 u |
7x2 = 14 u |
6x2 = 12 u |
Change |
- 11 u |
- 11 u |
|
After |
5x3 = 15 u |
1x3 = 3 u |
4x3 = 12 u |
(a)
Since Hilda and Jenson gave away the same number of cards, the difference in the number of cards between Hilda and Jenson 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 4 is 12.
Jenson's cards in May : Jenson's cards in June
14 : 3
(b)
Total number of cards in May
= 26 u + 14 u
= 40 u
Total number of cards in June
= 15 u + 3 u
= 18 u
Total cards in May : Total cards in June
40 : 18
(÷2)20 : 9
Answer(s): (a) 14 : 3; (b) 20 : 9