Zoe and Zara have some beads. If Zoe gives 15 beads to Zara, Zara will have 5 times the number of beads as Zoe. If Zara gives 20 beads to Zoe, Zoe will have
25 as many beads as Zara. How many beads does Zoe have at first?
|
Case 1 |
Case 2 |
|
Zoe |
Zara |
Zoe |
Zara |
Before |
7 u + 15 |
35 u - 15 |
12 u - 20 |
30 u + 20 |
Change |
- 15 |
+ 15 |
+ 20 |
- 20 |
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 Zoe had at first is the same in both cases.
12 u - 20 = 7 u + 15
12 u - 7 u = 15 + 20
5 u = 35
1 u = 7
Number of beads that Zoe had at first
= 7 u + 15
= 7 x 7 + 15
= 49 + 15
= 64
Answer(s): 64