MHB Please, I fast. I'm totally lost....

[Gabriel _J]

Problem: "There are 40 yellow, green and red candies in the basket. If all the yellow candies were replaced with green candies, there would be 7 times more green than red candies in the basket. If we replaced red candies with green candies, there would be 4 times more green candies in the basket than yellow candies. How many green candies are in the basket?"

Possible answers given: a)22 b)25 c)27 d)29

 

[Kansas Boy]

Let y be the number of yellow candies, g the number of green candies, r the number of red candies.

"There are 40 yellow, green and red candies in the basket."
So y+ g+ r= 40

"If all the yellow candies were replaced with green candies, there would be 7 times more green than red candies in the basket."
If all the yellow candies were replaced with green candies there would be y+ g green candies.
y+ g= 7r.

"If we replaced red candies with green candies, there would be 4 times more green candies in the basket than yellow candies."
If all the red candies were replaced with green candies there would be g+ r green candies.
g+ r= 4y.

From g+ r= 4y, g= 4y- r so y+ g+ r= y+ 4y- r+ r= 5y= 40. y= 8. y+ g= 8+ g= 7r, g= 7r- 8. r+ g= r+ 7r- 8= 8r- 8= 4y= 32. 8r=40. r= 40/8= 5. g= 7r- 8= 35- 8= 27.

There are 27 green candies.Check: If y= 8, g= 27, and r= 5 then
y+ g+ r= 8+ 27+ 5= 35+ 5= 40.
y+ g= 8+ 27= 35= 7(5)= 7r.
r+ g= 5+ 27= 32= 4(8)= 4y.