Dana and Marion have some puffs each. If Dana gives Marion 23 puffs, Dana will have
34 as many puffs as Marion. If Dana gives Marion 7 puffs, they will have an equal number of puffs. How many puffs does Marion have at first?
| |
Case 1 |
Case 2 |
| |
Dana |
Marion |
Dana |
Marion |
| Before |
3 u + 23 |
4 u - 23 |
3.5 u + 7 |
3.5 u - 7 |
| Change |
- 23 |
+ 23 |
- 7 |
+ 7 |
| After |
3 u |
4 u |
3.5 u |
3.5 u |
Total number of puffs that Dana and Marion have
= 3 u + 4 u
= 7 u
Number of puffs that Dana and Marion each has in the end is the same.
Number of puffs that Dana and Marion each has in the end in Case 2
= 7 u ÷ 2
= 3.5 u
Number of puffs that Dana had at first is the same in Case 1 and Case 2.
3.5 u + 7 = 3 u + 23
3.5 u - 3 u = 23 - 7
0.5 u = 16
1 u = 16 ÷ 0.5 = 32
Number of puffs that Marion has
= 4 u - 23
= 4 x 32 - 23
= 128 - 23
= 105
Answer(s): 105
