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An employee at a paint manufacturing plant is mixing highly pigmented paint with some paint that is less pigmented. In addition to a large supply of 11%-pigment paint, he also has 230 liters of 21%-pigment paint. How many liters of the 11%-pigment paint should he add to the 21%-pigment paint to generate a batch of 18%-pigment paint?

Respuesta :

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Answer:

98.57 L

Step-by-step explanation:

We can use the relation that

Volume of paint × concentration of pigment = amount of pigment  

or

V × c = P

If we call the three solutions 1, 2, and 3, then

       P₁ + P₂ = P₃

V₁c₁ + V₂c₂ = V₃c₃

Let x = the volume of 11 % paint.

Then

230 × 21 % + x × 11 % = (230 +x) × 18 %

                4830 + 11x = 4140 + 18x             Subtract 4140 from each side

                  690 + 11x = 18x                         Subtract 11x from each side

                          690 = 7x                            Divide each side by 7

                               x = 98.57 L

The employee should add 98.57 L of the 21 % pigment paint.

=====

Check:

230×21 + 11×98.57 = (230+98.57)×18

              4830 + 1084 = 328.57×18

                             5914 = 5914

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