Emily and Yen have some beads. If Emily gives 23 beads to Yen, Yen will have 4 times the number of beads as Emily. If Yen gives 82 beads to Emily, Emily will have
35 as many beads as Yen. How many beads does Emily have at first?
| |
Case 1 |
Case 2 |
| |
Emily |
Yen |
Emily |
Yen |
| Before |
8 u + 23 |
32 u - 23 |
15 u - 82 |
25 u + 82 |
| Change |
- 23 |
+ 23 |
+ 82 |
- 82 |
| After |
1x8 =
8 u |
4x8 =
32 u |
3x5 =
15 u |
5x5 =
25 u |
The total number of beads in both cases remains unchanged. Make the total number of beads in both cases the same. LCM of 5 and 8 is 40.
Number of beads that Emily had at first is the same in both cases.
15 u - 82 = 8 u + 23
15 u - 8 u = 23 + 82
7 u = 105
1 u = 15
Number of beads that Emily had at first
= 8 u + 23
= 8 x 15 + 23
= 120 + 23
= 143
Answer(s): 143
