Tammy and Xandra have some tarts each. If Tammy gives Xandra 8 tarts, Tammy will have
27 as many tarts as Xandra. If Tammy gives Xandra 5 tarts, they will have an equal number of tarts. How many tarts does Tammy have at first?
| |
Case 1 |
Case 2 |
| |
Tammy |
Xandra |
Tammy |
Xandra |
| Before |
2 u + 8 |
7 u - 8 |
4.5 u + 5 |
4.5 u - 5 |
| Change |
- 8 |
+ 8 |
- 5 |
+ 5 |
| After |
2 u |
7 u |
4.5 u |
4.5 u |
Total number of tarts that Tammy and Xandra have
= 2 u + 7 u
= 9 u
Number of tarts that Tammy and Xandra each has in the end is the same.
Number of tarts that Tammy and Xandra each has in the end in Case 2
= 9 u ÷ 2
= 4.5 u
Number of tarts that Tammy had at first is the same in Case 1 and Case 2.
4.5 u + 5 = 2 u + 8
4.5 u - 2 u = 8 - 5
0.5 u = 3
1 u = 3 ÷ 0.5 = 6
Number of tarts that Tammy has
= 2 u + 8
= 2 x 6 + 8
= 12 + 8
= 20
Answer(s): 20
