Yen and Diana have some puffs each. If Yen gives Diana 28 puffs, Yen will have
12 as many puffs as Diana. If Yen gives Diana 9 puffs, they will have an equal number of puffs. How many puffs does Diana have at first?
| |
Case 1 |
Case 2 |
| |
Yen |
Diana |
Yen |
Diana |
| Before |
1 u + 28 |
2 u - 28 |
1.5 u + 9 |
1.5 u - 9 |
| Change |
- 28 |
+ 28 |
- 9 |
+ 9 |
| After |
1 u |
2 u |
1.5 u |
1.5 u |
Total number of puffs that Yen and Diana have
= 1 u + 2 u
= 3 u
Number of puffs that Yen and Diana each has in the end is the same.
Number of puffs that Yen and Diana each has in the end in Case 2
= 3 u ÷ 2
= 1.5 u
Number of puffs that Yen had at first is the same in Case 1 and Case 2.
1.5 u + 9 = 1 u + 28
1.5 u - 1 u = 28 - 9
0.5 u = 19
1 u = 19 ÷ 0.5 = 38
Number of puffs that Diana has
= 2 u - 28
= 2 x 38 - 28
= 76 - 28
= 48
Answer(s): 48
