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Tough and Tricky questions: Word Problems.

A certain violet paint contains 30 percent blue pigment and 70 percent red pigment by weight. A certain green paint contains 50 percent blue pigment and 50 percent yellow pigment. When these paints are mixed to produce a brown paint, the brown paint contains 40 percent blue pigment. If the brown paint weighs 10 grams, then the red pigment contributes how many grams of that weight?

A. 2.8

B. 3.5

C. 4.2

D. 5

E. 7

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We are given that a certain violet paint contains 30 percent blue pigment and 70 percent red pigment, and that a certain green paint contains 50 percent blue and 50 percent yellow pigment. When the violet and green paints are mixed together, they become a brown paint with 40 percent blue pigment, and the brown paint weighs 10 grams. We need to determine the weight of the red pigment contained in the 10 grams of brown paint.

To determine the weight of the red pigment in the brown paint, we need to know the weight of the violet and green paints. Since neither weight is given, we can let x be the weight of the violet paint in grams. Since the weight of brown paint (i.e., the violet and green paints mixed) is 10 grams, the weight of the green paint is 10 - x grams.

Since 30 percent of the violet paint is the blue pigment, of the x grams of violet paint, 0.3x = the weight of the blue pigment. Similarly, since 50 percent of the green paint is the blue pigment, of the 10 - x grams of green paint, 0.5(10 - x) = the weight of the blue pigment. Finally, since 40 percent of the brown paint is the blue pigment, of the 10 grams of brown paint, 0.4(10) = 4 is the weight of the blue pigment in the entire mixture. Thus, we can set up the following equation and solve for x:

0.3x + 0.5(10 - x) = 4

3x + 5(10 - x) = 40

3x + 50 - 5x = 40

-2x = -10

x = 5

Recall that x is the weight of the violet paint. Since the violet paint is 5 grams, and 70 percent of it is the red pigment, the red pigment is 0.7(5) = 3.5 grams.

Answer: B

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