In a bag, the ratio of the number of grey beads to the number of purple beads was 1 : 3. Each time, 4 grey and 7 purple beads were taken out of the bag. A while later, only 120 purple beads were left in the bag. What was the total number of beads in the bag at first?
|
Grey beads |
Purple beads |
Before |
1x4 = 4 u |
3x4 = 12 u |
Change |
- 4 u |
- 7 u |
After |
0 |
120 |
Since there is no grey beads left, this means that the number of grey marbles at first is the same as the number of grey marbles taken out.
Make the number of grey beads at first and taken out the same. LCM of 1 and 4 is 4.
Number of purple beads in the end
= 12 u - 7 u
= 5 u
5 u = 120
1 u = 120 ÷ 5 = 24
Total number of beads in the bag at first
= 4 u + 12 u
= 16 u
= 16 x 24
= 384
Answer: 384