Ivory and Jean have some marbles. If Ivory gives 18 marbles to Jean, Jean will have 3 times the number of marbles as Ivory. If Jean gives 39 marbles to Ivory, Ivory will have
23 as many marbles as Jean. How many marbles does Ivory have at first?
|
Case 1 |
Case 2 |
|
Ivory |
Jean |
Ivory |
Jean |
Before |
5 u + 18 |
15 u - 18 |
8 u - 39 |
12 u + 39 |
Change |
- 18 |
+ 18 |
+ 39 |
- 39 |
After |
1x5 = 5 u |
3x5 = 15 u |
2x4 = 8 u |
3x4 = 12 u |
The total number of marbles in both cases remains unchanged. Make the total number of marbles in both cases the same. LCM of 4 and 5 is 20.
Number of marbles that Ivory had at first is the same in both cases.
8 u - 39 = 5 u + 18
8 u - 5 u = 18 + 39
3 u = 57
1 u = 19
Number of marbles that Ivory had at first
= 5 u + 18
= 5 x 19 + 18
= 95 + 18
= 113
Answer(s): 113