Cindy and Abi have some beads. If Cindy gives 27 beads to Abi, Abi will have 5 times the number of beads as Cindy. If Abi gives 48 beads to Cindy, Cindy will have
25 as many beads as Abi. How many beads does Cindy have at first?
|
Case 1 |
Case 2 |
|
Cindy |
Abi |
Cindy |
Abi |
Before |
7 u + 27 |
35 u - 27 |
12 u - 48 |
30 u + 48 |
Change |
- 27 |
+ 27 |
+ 48 |
- 48 |
After |
1x7 = 7 u |
5x7 = 35 u |
2x6 = 12 u |
5x6 = 30 u |
The total number of beads in both cases remains unchanged. Make the total number of beads in both cases the same. LCM of 6 and 7 is 42.
Number of beads that Cindy had at first is the same in both cases.
12 u - 48 = 7 u + 27
12 u - 7 u = 27 + 48
5 u = 75
1 u = 15
Number of beads that Cindy had at first
= 7 u + 27
= 7 x 15 + 27
= 105 + 27
= 132
Answer(s): 132