Ivan and Harry had 70 scones altogether. After Ivan ate ¹₃ of his scones and Harry ate 5 scones, the number of scones Harry had left was five times the number of scones Ivan had left. How many more scones did Harry have than Ivan at first?

	Ivan	Harry	Total
Before	3 u	10 u + 5	70
Change	- 1 u	- 5
After	2 u
Comparing Ivan and Harry in the end	1x2 = 2 u	5x2 = 10 u

The number of scones that Ivan had in the end is the same. Make the number of scones that Ivan had in the end the same.  LCM of 2 and 1 is 2.

Total number of scones at first
= 3 u + 10 u + 5
= 13 u + 5

13 u + 5 = 70
13 u = 70 - 5
13 u = 65 

1 u = 65 ÷ 13 = 5

Number of scones that Ivan had at first
= 3 u
= 3 x 5
= 15

Number of scones that Harry had at first
= 70 - 15
= 55

Number of scones that Harry had more than Ivan at first
= 55 - 15
= 40

Answer(s): 40