Opal and Ivory have some beads. If Opal gives 30 beads to Ivory, Ivory will have 4 times the number of beads as Opal. If Ivory gives 5 beads to Opal, Opal will have
35 as many beads as Ivory. How many beads does Opal have at first?
|
Case 1 |
Case 2 |
|
Opal |
Ivory |
Opal |
Ivory |
Before |
8 u + 30 |
32 u - 30 |
15 u - 5 |
25 u + 5 |
Change |
- 30 |
+ 30 |
+ 5 |
- 5 |
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 Opal had at first is the same in both cases.
15 u - 5 = 8 u + 30
15 u - 8 u = 30 + 5
7 u = 35
1 u = 5
Number of beads that Opal had at first
= 8 u + 30
= 8 x 5 + 30
= 40 + 30
= 70
Answer(s): 70