In January, Marion and Xavier had cards in the ratio 5 : 2. In February, each of them gave away the same number of cards. Marion then had five times as many cards as Xavier.
- Find the ratio of the number of cards Xavier 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.
| |
Marion |
Xavier |
Difference |
| Before |
5x4 =
20 u |
2x4 =
8 u |
3x4 =
12 u |
| Change |
- 5 u |
- 5 u |
|
| After |
5x3 =
15 u |
1x3 =
3 u |
4x3 =
12 u |
(a)
Since Marion and Xavier gave away the same number of cards, the difference in the number of cards between Marion and Xavier 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 3 and 4 is 12.
Xavier's cards in January : Xavier's cards in February
8 : 3
(b)
Total number of cards in January
= 20 u + 8 u
= 28 u
Total number of cards in February
= 15 u + 3 u
= 18 u
Total cards in January : Total cards in February
28 : 18
(÷2)14 : 9
Answer(s): (a) 8 : 3; (b) 14 : 9
