Rael and David had some pens in the ratio of 5 : 2. David and Michael had some pens in the ratio of 3 : 1. Rael sold 84 pens to Michael and ended up with half the number of pens David had. How many pens did Michael have in the end?
| Rael |
David |
Michael |
| 5x3 |
2x3 |
|
| |
3x2 |
1x2 |
| 15 u |
6 u |
2 u |
The number of pens that David had at first is repeated. Make the number of pens that David had at first the same. LCM of 2 and 3 is 6.
| |
Rael |
David |
Michael |
| Before |
15 u |
6 u |
2 u |
| Change |
- 84 |
|
+ 84 |
| After |
3 u |
6 u |
2 u + 84 |
Number of pens that Rael had in the end
= 6 u ÷ 2
= 3 u
Number of pens that Rael sold to Michael
= 15 u - 3 u
= 12 u
12 u = 84
1 u = 84 ÷ 12 = 7
Number of pens that Michael had in the end
= 2 u + 84
= 2 x 7 + 84
= 14 + 84
= 98
Answer(s): 98
