Solution to a Dicey Problem

Okay, let me reiterate the problem.  Three dice (red, blue, and green) are tossed and the values noted.  Then we perform the following operations on the values.  Start with red: multiply the red value by 2 then add 5 then then multiply this result by 5.  Now add in the value of the blue and multiply by 10.  Now add in the green.

Your result is 484.

What are the original values of the dice?

Solution Red = 2, Blue = 3, Green = 4

Why that's amazing you say.  How did you ever figure that out?

Funny you should ask.  

Assign variables to the values of the dice; Red = a, Blue = b, Green = c.  Now just follow the directions.

Multiply red by 2     2a

Add 5    2a + 5

Multiply this by 5    5(2a + 5) = 10a + 25

Add in Blue     10a + 25 + b

Multiply by 10     10(10a + 25 + b) = 100a + 250 + 10b

Add in green 100a + 10b + c +250

This equals 484    100a + 10b + c + 250 = 484

Subtract 250 from both sides    100a + 10b + c = 234

But the left hand side is the natural form of a three digit number (hundred, tens, ones)

Sooooooooo a = 2, b = 3, c = 4

And we could do this for any three values on the dice.  Try it for yourself.