Diana and Erika have some puffs each. If Diana gives Erika 28 puffs, Diana will have
23 as many puffs as Erika. If Diana gives Erika 8 puffs, they will have an equal number of puffs. How many puffs does Erika have at first?
| |
Case 1 |
Case 2 |
| |
Diana |
Erika |
Diana |
Erika |
| Before |
2 u + 28 |
3 u - 28 |
2.5 u + 8 |
2.5 u - 8 |
| Change |
- 28 |
+ 28 |
- 8 |
+ 8 |
| After |
2 u |
3 u |
2.5 u |
2.5 u |
Total number of puffs that Diana and Erika have
= 2 u + 3 u
= 5 u
Number of puffs that Diana and Erika each has in the end is the same.
Number of puffs that Diana and Erika each has in the end in Case 2
= 5 u ÷ 2
= 2.5 u
Number of puffs that Diana had at first is the same in Case 1 and Case 2.
2.5 u + 8 = 2 u + 28
2.5 u - 2 u = 28 - 8
0.5 u = 20
1 u = 20 ÷ 0.5 = 40
Number of puffs that Erika has
= 3 u - 28
= 3 x 40 - 28
= 120 - 28
= 92
Answer(s): 92
