Cathy and Min have some puffs each. If Cathy gives Min 15 puffs, Cathy will have
27 as many puffs as Min. If Cathy gives Min 6 puffs, they will have an equal number of puffs. How many puffs does Cathy have at first?
| |
Case 1 |
Case 2 |
| |
Cathy |
Min |
Cathy |
Min |
| Before |
2 u + 15 |
7 u - 15 |
4.5 u + 6 |
4.5 u - 6 |
| Change |
- 15 |
+ 15 |
- 6 |
+ 6 |
| After |
2 u |
7 u |
4.5 u |
4.5 u |
Total number of puffs that Cathy and Min have
= 2 u + 7 u
= 9 u
Number of puffs that Cathy and Min each has in the end is the same.
Number of puffs that Cathy and Min each has in the end in Case 2
= 9 u ÷ 2
= 4.5 u
Number of puffs that Cathy had at first is the same in Case 1 and Case 2.
4.5 u + 6 = 2 u + 15
4.5 u - 2 u = 15 - 6
0.5 u = 9
1 u = 9 ÷ 0.5 = 18
Number of puffs that Cathy has
= 2 u + 15
= 2 x 18 + 15
= 36 + 15
= 51
Answer(s): 51
