In January, Xandra and Riordan had cards in the ratio 11 : 4. In February, each of them gave away the same number of cards. Xandra then had five times as many cards as Riordan.
- Find the ratio of the number of cards Riordan 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.
| |
Xandra |
Riordan |
Difference |
| Before |
11x4 =
44 u |
4x4 =
16 u |
7x4 =
28 u |
| Change |
- 9 u |
- 9 u |
|
| After |
5x7 =
35 u |
1x7 =
7 u |
4x7 =
28 u |
(a)
Since Xandra and Riordan gave away the same number of cards, the difference in the number of cards between Xandra and Riordan 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 7 and 4 is 28.
Riordan's cards in January : Riordan's cards in February
16 : 7
(b)
Total number of cards in January
= 44 u + 16 u
= 60 u
Total number of cards in February
= 35 u + 7 u
= 42 u
Total cards in January : Total cards in February
60 : 42
(÷6)10 : 7
Answer(s): (a) 16 : 7; (b) 10 : 7
