At first, Cole, Natalie and Will had some lollipops in the ratio 8 : 6 : 7 respectively. Cole had 400 lollipops. Then he gave all his lollipops to Natalie and Will. After receiving the lollipops from Cole, Natalie and Will had the same number of lollipops. How many lollipops did Natalie receive from Cole?

	Cole	Natalie	Will	Total
Before	8x2 = 16 u	6x2 = 12 u	7x2 = 14 u	21x2 = 42 u
Change	- 8 u	+ 8 u
After	0	1x21 = 21 u	1x21 = 21 u	2x21 = 42 u

The total number of lollipops remains unchanged. Make the total number of lollipops the same.  LCM of 2 and 21 is 42.

Total number of lollipops = 42 u

Number of lollipops that Natalie had in the end 
= 42 u ÷ 2
= 21 u

Number of lollipops that Cole had at first = 8 u 

8 u = 400

1 u = 400 ÷ 8 = 50

Number of lollipops that Natalie received from Cole
= 21 u - 12 u
= 9 u
= 9 x 50
= 450

Answer(s): 450