Yoko and Erika have some coins. If Yoko gives 11 coins to Erika, Erika will have 4 times the number of coins as Yoko. If Erika gives 16 coins to Yoko, Yoko will have
25 as many coins as Erika. How many coins does Yoko have at first?
|
Case 1 |
Case 2 |
|
Yoko |
Erika |
Yoko |
Erika |
Before |
7 u + 11 |
28 u - 11 |
10 u - 16 |
25 u + 16 |
Change |
- 11 |
+ 11 |
+ 16 |
- 16 |
After |
1x7 = 7 u |
4x7 = 28 u |
2x5 = 10 u |
5x5 = 25 u |
The total number of coins in both cases remains unchanged. Make the total number of coins in both cases the same. LCM of 5 and 7 is 35.
Number of coins that Yoko had at first is the same in both cases.
10 u - 16 = 7 u + 11
10 u - 7 u = 11 + 16
3 u = 27
1 u = 9
Number of coins that Yoko had at first
= 7 u + 11
= 7 x 9 + 11
= 63 + 11
= 74
Answer(s): 74