Logic Word Problems-need a faster method!

Sep 2008
Hey. this is on the Kaplan book page 135

A vending machine dispenses gumballs in a regularly repeating cycle of 10 different colors. If a quarter buys 3 gumballs, what is the minimum amount of money that must be spent before 3 gumballs of the same color are dispensed?

The correct answer is 1.75

Instead of labeling all the colors, is there a faster way?

Oct 2008
You know that you need 3 of the same color, and every cycle will give you another one of the same color. If you want 3 of every color, you would need 30 gumballs. However, you only need 3 of 1 color, which means 2 of everything else. so 2x9 +3 = 21. 21 gumballs divided by 3 is 7 quarters, or $1.75.