Mark and Elijah shared some pens in the ratio of 3 : 7. After both each gave away 10 pens to their cousin, the ratio of the number of pens Mark had to the total number of pens left was 1 : 5. How many pens did the two boys have at first?
| |
Mark |
Elijah |
Difference |
| Before |
3x3 =
9 u |
7x3 =
21 u |
4x3 =
12 u |
| Change |
- 10 |
- 10 |
|
| After |
1x4 =
4 u |
4x4 =
16 u |
3x4 =
12 u |
Number of pens that Mark and Elijah each gave to their cousin is the same.
The difference in the number of pens at first and in the end between Mark and Elijah remains unchanged. Make the difference in the number of pens the same. LCM of 4 and 3 is 12.
Number of pens that Mark gave to their cousin
= 9 u - 4 u
= 5 u
5 u = 10
1 u = 10 ÷ 5 = 2
Number of pens that the two boys had at first
= 9 u + 21 u
= 30 u
= 30 x 2
= 60
Answer(s): 60
