Usha and Sarah have some coins. If Usha gives 32 coins to Sarah, Sarah will have 4 times the number of coins as Usha. If Sarah gives 17 coins to Usha, Usha will have
35 as many coins as Sarah. How many coins does Usha have at first?
| |
Case 1 |
Case 2 |
| |
Usha |
Sarah |
Usha |
Sarah |
| Before |
8 u + 32 |
32 u - 32 |
15 u - 17 |
25 u + 17 |
| Change |
- 32 |
+ 32 |
+ 17 |
- 17 |
| After |
1x8 =
8 u |
4x8 =
32 u |
3x5 =
15 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 8 is 40.
Number of coins that Usha had at first is the same in both cases.
15 u - 17 = 8 u + 32
15 u - 8 u = 32 + 17
7 u = 49
1 u = 7
Number of coins that Usha had at first
= 8 u + 32
= 8 x 7 + 32
= 56 + 32
= 88
Answer(s): 88
