Sam and Luis shared some pens in the ratio of 5 : 8. After both each gave away 77 pens to their sister, the ratio of the number of pens Sam had to the total number of pens left was 1 : 4. How many pens did the two boys have at first?
| |
Sam |
Luis |
Difference |
| Before |
5x2 =
10 u |
8x2 =
16 u |
3x2 =
6 u |
| Change |
- 77 |
- 77 |
|
| After |
1x3 =
3 u |
3x3 =
9 u |
2x3 =
6 u |
Number of pens that Sam and Luis each gave to their sister is the same.
The difference in the number of pens at first and in the end between Sam and Luis remains unchanged. Make the difference in the number of pens the same. LCM of 3 and 2 is 6.
Number of pens that Sam gave to their sister
= 10 u - 3 u
= 7 u
7 u = 77
1 u = 77 ÷ 7 = 11
Number of pens that the two boys had at first
= 10 u + 16 u
= 26 u
= 26 x 11
= 286
Answer(s): 286
