Three boxes, C, A and B, contained 266 marbles. Ben added some marbles into Box C and the number of marbles in Box C tripled. He took out half of the number of marbles from Box A and added another 94 marbles into Box B. As a result, the ratio of the number of marbles in Box C, Box A and Box B became 9 : 4 : 7. What was the ratio of the number of marbles in Box A to the total number of marbles in Box C and Box B at first? Give the answer in its lowest term.
| |
Box C |
Box A |
Box B |
Total |
| Before |
1x3 =
3 u |
2x4 =
8 u |
7 u - 94 |
266 |
| Change |
+ 2x3 =
+ 6 u |
- 1x4 =
- 4 u |
+ 94 |
|
| After |
3x3 =
9 u |
1x4 =
4 u |
|
|
Comparing the
3 boxes |
9 u |
4 u |
7 u |
|
The number of marbles in Box C in the end is repeated. Make the number of marbles in Box C in the end the same. LCM of 3 and 9 is 9.
The number of marbles in Box A in the end is repeated. Make the number of marbles in Box A in the end the same. LCM of 1 and 4 is 4.
Total number of marbles at first
= 3 u + 8 u + 7 u - 94
= 18 u - 94
18 u - 94 = 266
18 u = 266 + 94
18 u = 360
1 u = 360 ÷ 18 = 20
Number of marbles in Box A at first
= 8 u
= 8 x 20
= 160
Number of marbles in Box C and Box B at first
= 266 - 160
= 106
Box A : Box C and Box B
160 : 106
(÷2)80 : 53
Answer(s): 80 : 53
