Problem #27

Posted on April 1, 2010 | 1 Comment

In the game Combat, a red army is worth 10 points, a blue army is worth 3 points, and a white army is worth 1 point. While I am playing I notice that the value of my red armies is worth 40 points more than the total value of my blue and white armies. Also, the number of red armies is one-third the total number of blue and white armies and all of my armies are worth a total of 240 points. How many total armies do I have?

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One Response to Problem #27

Sterling | April 9, 2010 at 20:11 | Reply

The total value of the red armies must be 140 points (so that blue + white is 100). Hence there are 14 red armies.

There are three times as many blue and white armies as red, so there are a total of 42. Since they have a value of 100, 29 must be blue and 13 must be white (because $29\times 3 + 13\times 1 = 100$ and $29 + 13 = 42$ ).

Hence the total number of armies is $14 + 29 + 13 = 56$ .