SOLUTION: Food Mixtures A pastry chef created a 30-ounce sugar solution that was 28% sugar from a 20% sugar solution and a 40% sugar solution. How much of the 20% sugar solution and how

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Food Mixtures A pastry chef created a 30-ounce sugar solution that was 28% sugar from a 20% sugar solution and a 40% sugar solution. How much of the 20% sugar solution and how       Log On


   



Question 1054174: Food Mixtures A pastry chef created a 30-ounce sugar solution that was 28% sugar from a 20% sugar solution and a 40% sugar solution.
How much of the 20% sugar solution and how much of the 40% sugar solution were used?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ounces of the 20% solution needed
Let +b+ = ounces of the 40% solution needed
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(1) +a+%2B+b+=+30+
(2) +%28+.2a+%2B+.4b+%29+%2F+30+=+.28+
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(2) +.2a+%2B+.4b+=+.28%2A30+
(2) +.2a+%2B+.4b+=+8.4+
(2) +2a+%2B+4b+=+84+
Multiply both sides of (1) by +2+ and
subtract (1) from (2)
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(2) +2a+%2B+4b+=+84+
(1) +-2a+-+2b+=+-60+
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+2b+=+24+
+b+=+12+
and
(1) +a+%2B+12+=+30+
(1) +a+=+18+
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18 ounces of the 20% solution are needed
12 ounces of the 40% solution are needed
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check:
(2) +%28+.2a+%2B+.4b+%29+%2F+30+=+.28+
(2) +%28+.2%2A18+%2B+.4%2A12+%29+%2F+30+=+.28+
(2) +%28+3.6+%2B+4.8+%29+%2F+30+=+.28+
(2) +8.4+=+.28%2A30+
(2) +8.4+=+8.4+
OK