Opal and Marion have some tarts each. If Opal gives Marion 23 tarts, Opal will have
38 as many tarts as Marion. If Opal gives Marion 17 tarts, they will have an equal number of tarts. How many tarts does Opal have at first?
| |
Case 1 |
Case 2 |
| |
Opal |
Marion |
Opal |
Marion |
| Before |
3 u + 23 |
8 u - 23 |
5.5 u + 17 |
5.5 u - 17 |
| Change |
- 23 |
+ 23 |
- 17 |
+ 17 |
| After |
3 u |
8 u |
5.5 u |
5.5 u |
Total number of tarts that Opal and Marion have
= 3 u + 8 u
= 11 u
Number of tarts that Opal and Marion each has in the end is the same.
Number of tarts that Opal and Marion each has in the end in Case 2
= 11 u ÷ 2
= 5.5 u
Number of tarts that Opal had at first is the same in Case 1 and Case 2.
5.5 u + 17 = 3 u + 23
5.5 u - 3 u = 23 - 17
0.5 u = 6
1 u = 6 ÷ 0.5 = 12
Number of tarts that Opal has
= 3 u + 23
= 3 x 12 + 23
= 36 + 23
= 59
Answer(s): 59
