Gavin, Colin and Dan share some sweets in the ratio 7:3:2. Gavin gets 75 more sweets than Dan. How many sweets does Colin get?

45 sweets.

Step-by-step explanation:

Gavin gets 7 (7+3+2) = 7/12 of the sweets.

Dan gets 2 / 12 so Gavin gets 7/2 times as much as Dan

Let Dan get x sweets then

x + 75 = 7x / 2

7x/2 - x = 75

5x/2 = 75

x = 75 * 2/5 = 30 sweets.

So Dan gets 30 sweets, Gavin gets 105 sweets and Colin gets 3/2 * 30

= 45 sweets.