SOLUTION: One mixture contains 20% sugar and 60% salt while another contains 50% sugar and 30% salt. How many cups of each mixture should you combine so that the result contains 8 cups of su

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Question 1145311: One mixture contains 20% sugar and 60% salt while another contains 50% sugar and 30% salt. How many cups of each mixture should you combine so that the result contains 8 cups of sugar and 6 cups of salt?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


x = cups of the first mixture
y = cups of the second mixture

sugar equation: 0.2x%2B0.5y+=+8
salt equation: 0.6x%2B0.3y+=+6

Solve by elimination: multiply the first equation by 3 and subtract the second equation.
   0.6x + 1.5y = 24
   0.6x + 0.3y =  6
  ------------------
          1.2y = 18

y = 18/1.2 = 15

Substitute y=15 in one of the original equations:

0.2x%2B0.5%2815%29+=+8
0.2x%2B7.5+=+8
0.2x+=+0.5
x+=+0.5%2F0.2+=+2.5

ANSWER: 2.5 cups of the first mixture and 15 cups of the second.

CHECK:
sugar: 0.2(2.5)+0.5(15) = 0.5+7.5 = 8
salt: 0.6(2.5)+0.3(15) = 1.5+4.5 = 6