An illustration set in a warmly lit casual restaurant, with a wooden countertop. On the countertop is a prominent glass bowl filled with various colored mints. There are three friends, a Caucasian man Sean, a Middle-Eastern man Fred, and a South Asian man Gene, standing near the bowl, each having a perplexed expression. Sean is seen with his hand about to return four mints back into the bowl, Fred is holding three mints over the bowl, and Gene is throwing back two green mints into the bowl. The composition suggests they each took part of the mints. The bowl appears to have only 17 mints left.

After dinner, three friends at a restaurant paid their bill and noticed a bowl of mints on the front counter. Sean took one-third of the mints but returned four because he had a momentary pang of guilt. Fred then took one-fourth of what was left but returned

three for similar reasons. Gene then took half of the remainder but threw two green ones back in the bowl. The bowl had only 17 mints left over when they were done. How many mints were originally in the bowl?

48

1/3 of 48 is 16, 16-4= 12 mints took by Sean
36 mints left in the bowl
1/4 of 36 is 9, 9-3= 6 mints took by Fred
30 mints left
1/2 of 30 is 15, 15-2= 13 mints took by Gene
So, There are 48 mints were originally in the bowl.

Well, let's use our detective skills and do some minty math!

We know that there were 17 mints left in the bowl at the end. So, let's work our way backwards to figure out how many mints were originally in the bowl.

Gene took half of whatever was left, but then threw two green mints back in. So, whatever was left after Sean and Fred would be the total amount Gene took, plus the two green mints.

Fred took one-fourth of what was left, but then returned three. So, whatever was left after Sean would be the total amount Fred took, plus the three mints he put back.

Sean took one-third of the mints in the beginning, but then returned four. So, whatever was left at the end would be the original amount Sean took, plus the four mints he put back.

Now, let's add all those amounts to find the original number of mints:

17 (remaining) + 2 (green thrown in by Gene) + 3 (mints returned by Fred) + 4 (mints returned by Sean) = 26

Therefore, there were originally 26 mints in the bowl.

I hope this minty math journey brought a smile to your face!

To solve this problem, let's work backwards.

We know that after all the friends took their share and returned some, there were 17 mints left in the bowl. Let's call this final number of mints "x".

Before Gene threw two green mints back, there were "x + 2" mints in the bowl. We can determine this by retracing Gene's actions. We know that Gene took half of the remainder, so the number of mints before Gene took his share was twice as many as the number of mints after he threw two green mints back.

Before Fred returned three mints, there were "2 * (x + 2)" mints in the bowl. We can determine this by retracing Fred's actions. We know that Fred took one-fourth of what was left, so the number of mints before Fred took his share was four times as many as the number of mints after he returned three mints.

Before Sean returned four mints, there were "4 * (2 * (x + 2))" mints in the bowl. We can determine this by retracing Sean's actions. We know that Sean took one-third of the mints initially, so the number of mints before Sean took his share was three times as many as the number of mints after he returned four mints.

Therefore, we have the equation:

4 * (2 * (x + 2)) = 3 * (4 * (2 * (x + 2)) + 3) + 4

Now, we can solve for "x" to find the original number of mints in the bowl.

48 mints were originally in the bowl.

17-2=15*2=30-3=27/3=9+27=36-4=32/2=18+32=48