Neave and Luis shared some erasers in the ratio of 5 : 7. After both each gave away 63 erasers to their cousin, the ratio of the number of erasers Neave had to the total number of erasers left was 1 : 6. How many erasers did the two boys have at first?

	Neave	Luis	Difference
Before	5x2 = 10 u	7x2 = 14 u	2x2 = 4 u
Change	- 63	- 63
After	1x1 = 1 u	5x1 = 5 u	4x1 = 4 u

Number of erasers that Neave and Luis each gave to their cousin is the same.

The difference in the number of erasers at first and in the end between Neave and Luis remains unchanged.  Make the difference in the number of erasers the same.  LCM of 2 and 4 is 4.

Number of erasers that Neave gave to their cousin
= 10 u - 1 u
= 9 u

9 u = 63

1 u = 63 ÷ 9 = 7

Number of erasers that the two boys had at first
= 10 u + 14 u
= 24 u
= 24 x 7
= 168

Answer(s): 168