Joelle and Tina have some beads. If Joelle gives 37 beads to Tina, Tina will have 5 times the number of beads as Joelle. If Tina gives 68 beads to Joelle, Joelle will have
23 as many beads as Tina. How many beads does Joelle have at first?
| |
Case 1 |
Case 2 |
| |
Joelle |
Tina |
Joelle |
Tina |
| Before |
5 u + 37 |
25 u - 37 |
12 u - 68 |
18 u + 68 |
| Change |
- 37 |
+ 37 |
+ 68 |
- 68 |
| After |
1x5 =
5 u |
5x5 =
25 u |
2x6 =
12 u |
3x6 =
18 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 5 is 30.
Number of beads that Joelle had at first is the same in both cases.
12 u - 68 = 5 u + 37
12 u - 5 u = 37 + 68
7 u = 105
1 u = 15
Number of beads that Joelle had at first
= 5 u + 37
= 5 x 15 + 37
= 75 + 37
= 112
Answer(s): 112
