Three cartons, B, C and A, contained 214 marbles. Elijah added some marbles into Carton B and the number of marbles in Carton B tripled. He took out half of the number of marbles from Carton C and removed 19 marbles from Carton A. As a result, the ratio of the number of marbles in Carton B, Carton C and Carton A became 6 : 2 : 7. What was the ratio of the number of marbles in Carton A to the total number of marbles in Carton B and Carton C at first? Give the answer in its lowest term.
|
Carton B |
Carton C |
Carton A |
Total |
Before |
1x2 = 2 u |
2x2 = 4 u |
7 u + 19 |
214 |
Change |
+ 2x2 = + 4 u |
- 1x2 = - 2 u |
- 19 |
|
After |
3x2 = 6 u |
1x2 = 2 u |
|
|
Comparing the 3 cartons |
6 u
|
2 u |
7 u |
|
The number of marbles in Carton B in the end is the same. Make the number of marbles in Carton B in the end the same. LCM of 3 and 6 is 6.
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 1 and 2 is 2.
Total number of marbles at first
= 2 u + 4 u + 7 u + 19
= 13 u + 19
13 u + 19 = 214
13 u = 214 - 19
13 u = 195
1 u = 195 ÷ 13 = 15
Number of marbles in Carton A at first
= 7 u + 19
= 7 x 15 + 19
= 105 + 19
= 124
Number of marbles in Carton B and Carton C at first
= 214 - 124
= 90
Carton A : Carton B and Carton C
124 : 90
(÷2)62 : 45
Answer(s): 62 : 45