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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?

Re: A certain violet paint contains 30 percent blue pigment and 70 percent [#permalink]

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03 Nov 2014, 08:01

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10 Grams of combined mixture and 40% blue pigment means that the mixtures were mixed 50% each. Thus 5 grams a piece. Out of the 5 grams of the violet paint, 70% is red. Therefore, 5*.7 = 3.5Grams of red pigment

Re: A certain violet paint contains 30 percent blue pigment and 70 percent [#permalink]

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03 Nov 2014, 22:29

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Bunuel wrote:

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

Kudos for a correct solution.

Say Violet Paint = 100 Litres (30 Litres Blue + 70 Litres Red)

Say Green Paint = 100 Litres (50 Litres Blue + 50 Litres Yellow)

Total Mixture would be = 200 Litres (80 Litres Blue + 70 Litres Red + 50 Litres Yellow)

Re: A certain violet paint contains 30 percent blue pigment and 70 percent [#permalink]

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01 Feb 2016, 06:32

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Re: A certain violet paint contains 30 percent blue pigment and 70 percent [#permalink]

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11 Jan 2017, 06:24

There is an alternative way to come up with the conclusion that there must be equal amounts of green and violet paints in the mix. Since there is blue paint in both the violet and green paints, when we combine the two paints, the percentage of blue paint in the mix will be a weighted average of the percentages of blue in the violet paint and the percentage of blue in the green paint. For example, if there is twice as much violet as green in the brown mix, the percentage of blue in the violet will get double weighted. From looking at the numbers, however, 40% is exactly the simple average of the 30% blue in violet and the 50% blue in green. This means that there must be an equal amount of both paints in the mix.

Since there are equal amounts of violet and green paint in the 10 grams of brown mixture, there must be 5 grams of each. The violet paint is 70% red, so there must be (.7)(5) = 3.5 grams of red paint in the mix.

A certain violet paint contains 30 percent blue pigment and 70 percent [#permalink]

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11 Jan 2017, 12:24

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Bunuel wrote:

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

Kudos for a correct solution.

let v=grams of violet paint .3v+.5(10-v)=.4*10 v=5 grams 5*.7=3.5 grams of red pigment B

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

\

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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