There are only blue sweets green sweets and red

The greatest possible number of red sweets is 28

Step-by-step explanation:

Let the common ratio between blue and red sweets be x

Then,

Number of blue sweets = 2x

Number of green sweets = 7x

If the common ratio between the green and red sweets be y

Then,

Number of green sweets = 3y

Number of red sweets = y

Here the number of green sweets must be equal

Therefore,

Also the sum of all of them is 140

Thus,

x should be a whole number

Therefore,  

And the sum of all the sweets will be 136

Therefore,

Thus the greatest possible number of red sweets is 28

Hope this helps.

i believe so, according to my "strange" way of figuring out weird math problems like this.