Three cartons, C, A and B, contained 118 beads. Daniel added some beads into Carton C and the number of beads in Carton C tripled. He took out half of the number of beads from Carton A and added another 22 beads into Carton B. As a result, the ratio of the number of beads in Carton C, Carton A and Carton B became 9 : 4 : 3. What was the ratio of the number of beads in Carton A to the total number of beads in Carton C and Carton B at first? Give the answer in its lowest term.
| |
Carton C |
Carton A |
Carton B |
Total |
| Before |
1x3 =
3 u |
2x4 =
8 u |
3 u - 22 |
118 |
| Change |
+ 2x3 =
+ 6 u |
- 1x4 =
- 4 u |
+ 22 |
|
| After |
3x3 =
9 u |
1x4 =
4 u |
|
|
Comparing the
3 cartons |
9 u |
4 u |
3 u |
|
The number of beads in Carton C in the end is repeated. Make the number of beads in Carton C in the end the same. LCM of 3 and 9 is 9.
The number of beads in Carton A in the end is repeated. Make the number of beads in Carton A in the end the same. LCM of 1 and 4 is 4.
Total number of beads at first
= 3 u + 8 u + 3 u - 22
= 14 u - 22
14 u - 22 = 118
14 u = 118 + 22
14 u = 140
1 u = 140 ÷ 14 = 10
Number of beads in Carton A at first
= 8 u
= 8 x 10
= 80
Number of beads in Carton C and Carton B at first
= 118 - 80
= 38
Carton A : Carton C and Carton B
80 : 38
(÷2)40 : 19
Answer(s): 40 : 19
