Xandra and Jane have some tarts each. If Xandra gives Jane 19 tarts, Xandra will have
18 as many tarts as Jane. If Xandra gives Jane 9 tarts, they will have an equal number of tarts. How many tarts does Xandra have at first?
| |
Case 1 |
Case 2 |
| |
Xandra |
Jane |
Xandra |
Jane |
| Before |
1 u + 19 |
8 u - 19 |
4.5 u + 9 |
4.5 u - 9 |
| Change |
- 19 |
+ 19 |
- 9 |
+ 9 |
| After |
1 u |
8 u |
4.5 u |
4.5 u |
Total number of tarts that Xandra and Jane have
= 1 u + 8 u
= 9 u
Number of tarts that Xandra and Jane each has in the end is the same.
Number of tarts that Xandra and Jane each has in the end in Case 2
= 9 u ÷ 2
= 4.5 u
Number of tarts that Xandra had at first is the same in Case 1 and Case 2.
4.5 u + 9 = 1 u + 19
4.5 u - 1 u = 19 - 9
0.5 u = 10
1 u = 10 ÷ 0.5 = 20
Number of tarts that Xandra has
= 1 u + 19
= 1 x 20 + 19
= 20 + 19
= 39
Answer(s): 39
