In a jar, the ratio of the number of yellow marbles to the number of black marbles was 1 : 4. Each time, 3 yellow and 6 black marbles were taken out of the jar. A while later, only 42 black marbles were left in the jar. What was the total number of marbles in the jar at first?
|
Yellow marbles |
Black marbles |
Before |
1x3 = 3 u |
4x3 = 12 u |
Change |
- 3 u |
- 6 u |
After |
0 |
42 |
Since there is no yellow marbles left, this means that the number of yellow marbles at first is the same as the number of yellow marbles taken out.
Make the number of yellow marbles at first and taken out the same. LCM of 1 and 3 is 3.
Number of black marbles in the end
= 12 u - 6 u
= 6 u
6 u = 42
1 u = 42 ÷ 6 = 7
Total number of marbles in the jar at first
= 3 u + 12 u
= 15 u
= 15 x 7
= 105
Answer: 105