In March, Penelope and Caden had cards in the ratio 7 : 6. In April, each of them gave away the same number of cards. Penelope then had five times as many cards as Caden.
- Find the ratio of the number of cards Caden 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.
| |
Penelope |
Caden |
Difference |
| Before |
7x4 =
28 u |
6x4 =
24 u |
1x4 =
4 u |
| Change |
- 23 u |
- 23 u |
|
| After |
5x1 =
5 u |
1x1 =
1 u |
4x1 =
4 u |
(a)
Since Penelope and Caden gave away the same number of cards, the difference in the number of cards between Penelope and Caden 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 4 is 4.
Caden's cards in March : Caden's cards in April
24 : 1
(b)
Total number of cards in March
= 28 u + 24 u
= 52 u
Total number of cards in April
= 5 u + 1 u
= 6 u
Total cards in March : Total cards in April
52 : 6
(÷2)26 : 3
Answer(s): (a) 24 : 1; (b) 26 : 3
