In January, Xuan and Zane had beads in the ratio 15 : 7. In February, each of them gave away the same number of beads. Xuan then had thrice as many beads as Zane.
- Find the ratio of the number of beads Zane had in January to the number of beads he had in February.
- Find the ratio of the total number of beads both had in January to the total number of beads both had in February.
| |
Xuan |
Zane |
Difference |
| Before |
15x1 =
15 u |
7x1 =
7 u |
8x1 =
8 u |
| Change |
- 3 u |
- 3 u |
|
| After |
3x4 =
12 u |
1x4 =
4 u |
2x4 =
8 u |
(a)
Since Xuan and Zane gave away the same number of beads, the difference in the number of beads between Xuan and Zane at first and in the end remains the same.
Make the difference in the number of beads at first and in the end the same. LCM of 8 and 2 is 8.
Zane's beads in January : Zane's beads in February
7 : 4
(b)
Total number of beads in January
= 15 u + 7 u
= 22 u
Total number of beads in February
= 12 u + 4 u
= 16 u
Total beads in January : Total beads in February
22 : 16
(÷2)11 : 8
Answer(s): (a) 7 : 4; (b) 11 : 8
