Hilda and Usha have some tarts each. If Hilda gives Usha 21 tarts, Hilda will have
18 as many tarts as Usha. If Hilda gives Usha 2 tarts, they will have an equal number of tarts. How many tarts does Usha have at first?
| |
Case 1 |
Case 2 |
| |
Hilda |
Usha |
Hilda |
Usha |
| Before |
1 u + 21 |
8 u - 21 |
4.5 u + 2 |
4.5 u - 2 |
| Change |
- 21 |
+ 21 |
- 2 |
+ 2 |
| After |
1 u |
8 u |
4.5 u |
4.5 u |
Total number of tarts that Hilda and Usha have
= 1 u + 8 u
= 9 u
Number of tarts that Hilda and Usha each has in the end is the same.
Number of tarts that Hilda and Usha each has in the end in Case 2
= 9 u ÷ 2
= 4.5 u
Number of tarts that Hilda had at first is the same in Case 1 and Case 2.
4.5 u + 2 = 1 u + 21
4.5 u - 1 u = 21 - 2
0.5 u = 19
1 u = 19 ÷ 0.5 = 38
Number of tarts that Usha has
= 8 u - 21
= 8 x 38 - 21
= 304 - 21
= 283
Answer(s): 283
