Hazel and Sarah have some pencils in the ratio 3 : 13. Hazel has 90 less pencils than Sarah. How many pencils must Sarah give to Hazel so that they will have the same number of pencils?
| |
Hazel |
Sarah |
Total |
| Before |
3 u |
13 u |
16 u |
| Change |
+ 5 u |
- 5 u |
|
After |
1x8 =
8 u |
1x8 =
8 u |
2x8 =
16 u |
The total number of pencils remains unchanged. Make the total number of pencils at first and in the end the same. LCM of 2 and 16 is 16.
Difference in the number of pencils at first
= 13 u - 3 u
= 10 u
10 u = 90
1 u = 90 ÷ 10 = 9
Number of pencils that each of them had in the end
= 16 u ÷ 2
= 8 u
Number of pencils that Sarah must give to Hazel
= 8 u - 3 u
= 5 u
= 5 x 9
= 45
Answer(s): 45
