Three boxes, C, A and B, contained 294 balls. Pierre added some balls into Box C and the number of balls in Box C tripled. He took out half of the number of balls from Box A and added another 26 balls into Box B. As a result, the ratio of the number of balls in Box C, Box A and Box B became 9 : 3 : 7. What was the ratio of the number of balls in Box A to the total number of balls 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 |
2x3 = 6 u |
7 u - 26 |
294 |
Change |
+ 2x3 = + 6 u |
- 1x3 = - 3 u |
+ 26 |
|
After |
3x3 = 9 u |
1x3 = 3 u |
|
|
Comparing the 3 boxes |
9 u |
3 u |
7 u |
|
The number of balls in Box C in the end is repeated. Make the number of balls in Box C in the end the same. LCM of 3 and 9 is 9.
The number of balls in Box A in the end is repeated. Make the number of balls in Box A in the end the same. LCM of 1 and 3 is 3.
Total number of balls at first
= 3 u + 6 u + 7 u - 26
= 16 u - 26
16 u - 26 = 294
16 u = 294 + 26
16 u = 320
1 u = 320 ÷ 16 = 20
Number of balls in Box A at first
= 6 u
= 6 x 20
= 120
Number of balls in Box C and Box B at first
= 294 - 120
= 174
Box A : Box C and Box B
120 : 174
(÷6)20 : 29
Answer(s): 20 : 29