Three cartons, C, A and B, contained 418 marbles. Oscar added some marbles into Carton C and the number of marbles in Carton C tripled. He took out half of the number of marbles from Carton A and removed 98 marbles from Carton B. As a result, the ratio of the number of marbles in Carton C, Carton A and Carton B became 9 : 4 : 5. What was the ratio of the number of marbles in Carton B to the total number of marbles in Carton C and Carton A at first? Give the answer in its lowest term.
|
Carton C |
Carton A |
Carton B |
Total |
Before |
1x3 = 3 u |
2x4 = 8 u |
5 u + 98 |
418 |
Change |
+ 2x3 = + 6 u |
- 1x4 = - 4 u |
- 98 |
|
After |
3x3 = 9 u |
1x4 = 4 u |
|
|
Comparing the 3 cartons |
9 u
|
4 u |
5 u |
|
The number of marbles in Carton C in the end is the same. Make the number of marbles in Carton C in the end the same. LCM of 3 and 9 is 9.
The number of marbles in Carton A in the end is the same. Make the number of marbles in Carton A in the end the same. LCM of 1 and 4 is 4.
Total number of marbles at first
= 3 u + 8 u + 5 u + 98
= 16 u + 98
16 u + 98 = 418
16 u = 418 - 98
16 u = 320
1 u = 320 ÷ 16 = 20
Number of marbles in Carton B at first
= 5 u + 98
= 5 x 20 + 98
= 100 + 98
= 198
Number of marbles in Carton C and Carton A at first
= 418 - 198
= 220
Carton B : Carton C and Carton A
198 : 220
(÷22)9 : 10
Answer(s): 9 : 10