Opal and Dana have some puffs each. If Opal gives Dana 18 puffs, Opal will have
34 as many puffs as Dana. If Opal gives Dana 8 puffs, they will have an equal number of puffs. How many puffs does Dana have at first?
| |
Case 1 |
Case 2 |
| |
Opal |
Dana |
Opal |
Dana |
| Before |
3 u + 18 |
4 u - 18 |
3.5 u + 8 |
3.5 u - 8 |
| Change |
- 18 |
+ 18 |
- 8 |
+ 8 |
| After |
3 u |
4 u |
3.5 u |
3.5 u |
Total number of puffs that Opal and Dana have
= 3 u + 4 u
= 7 u
Number of puffs that Opal and Dana each has in the end is the same.
Number of puffs that Opal and Dana each has in the end in Case 2
= 7 u ÷ 2
= 3.5 u
Number of puffs that Opal had at first is the same in Case 1 and Case 2.
3.5 u + 8 = 3 u + 18
3.5 u - 3 u = 18 - 8
0.5 u = 10
1 u = 10 ÷ 0.5 = 20
Number of puffs that Dana has
= 4 u - 18
= 4 x 20 - 18
= 80 - 18
= 62
Answer(s): 62
