In a bottle, the ratio of the number of yellow beads to the number of blue beads was 1 : 3. Each time, 4 yellow and 7 blue beads were taken out of the bottle. A while later, only 45 blue beads were left in the bottle. What was the total number of beads in the bottle at first?
| |
Yellow beads |
Blue beads |
| Before |
1x4 =
4 u |
3x4 =
12 u |
| Change |
- 4 u |
- 7 u |
| After |
0 |
45 |
Since there is no yellow beads 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 beads at first and taken out the same. LCM of 1 and 4 is 4.
Number of blue beads in the end
= 12 u - 7 u
= 5 u
5 u = 45
1 u = 45 ÷ 5 = 9
Total number of beads in the bottle at first
= 4 u + 12 u
= 16 u
= 16 x 9
= 144
Answer: 144
