Emily and Kathy have some puffs each. If Emily gives Kathy 19 puffs, Emily will have
14 as many puffs as Kathy. If Emily gives Kathy 13 puffs, they will have an equal number of puffs. How many puffs does Emily have at first?
| |
Case 1 |
Case 2 |
| |
Emily |
Kathy |
Emily |
Kathy |
| Before |
1 u + 19 |
4 u - 19 |
2.5 u + 13 |
2.5 u - 13 |
| Change |
- 19 |
+ 19 |
- 13 |
+ 13 |
| After |
1 u |
4 u |
2.5 u |
2.5 u |
Total number of puffs that Emily and Kathy have
= 1 u + 4 u
= 5 u
Number of puffs that Emily and Kathy each has in the end is the same.
Number of puffs that Emily and Kathy each has in the end in Case 2
= 5 u ÷ 2
= 2.5 u
Number of puffs that Emily had at first is the same in Case 1 and Case 2.
2.5 u + 13 = 1 u + 19
2.5 u - 1 u = 19 - 13
0.5 u = 6
1 u = 6 ÷ 0.5 = 12
Number of puffs that Emily has
= 1 u + 19
= 1 x 12 + 19
= 12 + 19
= 31
Answer(s): 31
