Erika and Fiona have some tarts each. If Erika gives Fiona 14 tarts, Erika will have
47 as many tarts as Fiona. If Erika gives Fiona 11 tarts, they will have an equal number of tarts. How many tarts does Erika have at first?
| |
Case 1 |
Case 2 |
| |
Erika |
Fiona |
Erika |
Fiona |
| Before |
4 u + 14 |
7 u - 14 |
5.5 u + 11 |
5.5 u - 11 |
| Change |
- 14 |
+ 14 |
- 11 |
+ 11 |
| After |
4 u |
7 u |
5.5 u |
5.5 u |
Total number of tarts that Erika and Fiona have
= 4 u + 7 u
= 11 u
Number of tarts that Erika and Fiona each has in the end is the same.
Number of tarts that Erika and Fiona each has in the end in Case 2
= 11 u ÷ 2
= 5.5 u
Number of tarts that Erika had at first is the same in Case 1 and Case 2.
5.5 u + 11 = 4 u + 14
5.5 u - 4 u = 14 - 11
0.5 u = 3
1 u = 3 ÷ 0.5 = 6
Number of tarts that Erika has
= 4 u + 14
= 4 x 6 + 14
= 24 + 14
= 38
Answer(s): 38
