In a bottle, the ratio of the number of gold beads to the number of red beads was 1 : 3. Each time, 3 gold and 7 red beads were taken out of the bottle. A while later, only 116 red beads were left in the bottle. What was the total number of beads in the bottle at first?
| |
Gold beads |
Red beads |
| Before |
1x3 =
3 u |
3x3 =
9 u |
| Change |
- 3 u |
- 7 u |
| After |
0 |
116 |
Since there is no gold beads left, this means that the number of gold marbles at first is the same as the number of gold marbles taken out.
Make the number of gold beads at first and taken out the same. LCM of 1 and 3 is 3.
Number of red beads in the end
= 9 u - 7 u
= 2 u
2 u = 116
1 u = 116 ÷ 2 = 58
Total number of beads in the bottle at first
= 3 u + 9 u
= 12 u
= 12 x 58
= 696
Answer: 696
