ExplanationChoose a smart number for the total number of shirts in the closest; this is a percent problem, so 100 is a good number to pick. Out of 100 shirts, half, or 50, are white.

You know 30% of the remaining shirts are gray.

If there are 50 white shirts, there are also 50 remaining shirts and so (0.3)(50) = 15 gray shirts. Therefore, there are 50 + 15 = 65 total shirts that are white or gray, and 100 – 65 = 35 shirts that are neither white nor gray. Since 35 out of 100 shirts are neither white nor gray, exactly 35% of the shirts are neither white nor gray.

Alternatively, use algebra, though that is trickier on a problem such as this one. Set a variable, such as x, for the total number of shirts. The number of white shirts is 0.5x and the remaining shirts would equal

x – 0.5x = 0.5x.

The number of gray shirts, then, is (0.5x)(0.3) = 0.15x. Thus, there are

0.5x + 0.15x = 0.65x white or gray shirts, and

x – 0.6x = 0.35x shirts that are neither white nor gray.

Therefore, 0.35x ÷ x = 0.35, or 35%.

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Sandy

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