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A family wants to make two shades of purple food coloring using exactly 30 tablespoons of red solution and two tablespoons of blue solution.
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They want their light purple color to have 2 % blue, and their dark purple to have 10 % blue.
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How much of each purple shade can they make? to figure this question out, let's give names to the numbers whose values we want to find, that is, the, amount of dark purple and light purple solutions, and then using those two variables, make two equations with those variables, and then solve those equations to find the values of those variables.
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And so let's call our variables x and y.
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X is the amount of light purple solution, and y is the amount of dark purple.
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Now we want to find equations to use.
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So how are x and y to the amount of blue solution, for example.
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Well, we know that 2 % of the light purple color plus 10 % of the dark purple color, the total amount of blue, is two tablespoons.
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And so one equation we can make is 2 % of x plus 10 % of y equals 2.
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Now, where can we find the other equation from? well, we could do the same thing.
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With red that we did with blue.
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That is, we could say that 98 % of the light purple solution is red, and 90 % of the dark purple is red, and so 98 % of x plus 90 % of y equals 30...