Zoe and Tina have some marbles. If Zoe gives 19 marbles to Tina, Tina will have 3 times the number of marbles as Zoe. If Tina gives 32 marbles to Zoe, Zoe will have
23 as many marbles as Tina. How many marbles does Zoe have at first?
|
Case 1 |
Case 2 |
|
Zoe |
Tina |
Zoe |
Tina |
Before |
5 u + 19 |
15 u - 19 |
8 u - 32 |
12 u + 32 |
Change |
- 19 |
+ 19 |
+ 32 |
- 32 |
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 Zoe had at first is the same in both cases.
8 u - 32 = 5 u + 19
8 u - 5 u = 19 + 32
3 u = 51
1 u = 17
Number of marbles that Zoe had at first
= 5 u + 19
= 5 x 17 + 19
= 85 + 19
= 104
Answer(s): 104