In May, Shiyun and Ethan had beads in the ratio 7 : 4. In June, each of them gave away the same number of beads. Shiyun then had thrice as many beads as Ethan.
- Find the ratio of the number of beads Ethan had in May to the number of beads he had in June.
- Find the ratio of the total number of beads both had in May to the total number of beads both had in June.
| |
Shiyun |
Ethan |
Difference |
| Before |
7x2 =
14 u |
4x2 =
8 u |
3x2 =
6 u |
| Change |
- 5 u |
- 5 u |
|
| After |
3x3 =
9 u |
1x3 =
3 u |
2x3 =
6 u |
(a)
Since Shiyun and Ethan gave away the same number of beads, the difference in the number of beads between Shiyun and Ethan 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 3 and 2 is 6.
Ethan's beads in May : Ethan's beads in June
8 : 3
(b)
Total number of beads in May
= 14 u + 8 u
= 22 u
Total number of beads in June
= 9 u + 3 u
= 12 u
Total beads in May : Total beads in June
22 : 12
(÷2)11 : 6
Answer(s): (a) 8 : 3; (b) 11 : 6
