In a jar, the ratio of the number of purple beads to the number of silver beads was 1 : 3. Each time, 3 purple and 6 silver beads were taken out of the jar. A while later, only 48 silver beads were left in the jar. What was the total number of beads in the jar at first?
| |
Purple beads |
Silver beads |
| Before |
1x3 =
3 u |
3x3 =
9 u |
| Change |
- 3 u |
- 6 u |
| After |
0 |
48 |
Since there is no purple beads left, this means that the number of purple marbles at first is the same as the number of purple marbles taken out.
Make the number of purple beads at first and taken out the same. LCM of 1 and 3 is 3.
Number of silver beads in the end
= 9 u - 6 u
= 3 u
3 u = 48
1 u = 48 ÷ 3 = 16
Total number of beads in the jar at first
= 3 u + 9 u
= 12 u
= 12 x 16
= 192
Answer: 192
