SOLUTION: one grade of oil has .50% of an additive. a higher grade has .75% of the additive. how many quarts of each must be used to have 250 quarts of a mixture with .65% of the additive?

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Question 1052044: one grade of oil has .50% of an additive. a higher grade has .75% of the additive. how many quarts of each must be used to have 250 quarts of a mixture with .65% of the additive?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = quarts of the .5 % oil
Let +b+ = quarts of the .75% oil
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(1) +a+%2B+b+=+250+ quarts
(2) +%28+.005a+%2B+.0075b+%29+%2F+250+=+.0065+
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(2) +.005a+%2B+.0075b+=+.0065%2A250+
(2) +.005a+%2B+.0075b+=+1.625+
(2) +50a+%2B+75b+=+16250+
(2) +2a+%2B+3b+=+650+
Multiply both sides of (1) by +2+ and
subtract (1) from (2)
(2) +2a+%2B+3b+=+650+
(1) +-2a+-+2b+=+-500+
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+b+=+150+
and
(1) +a+%2B+b+=+250+
(1) +a+%2B+150+=+250+
(1) +a+=+100+
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100 quarts of the .5 % oil are needed
150 quarts of the .75% oil are needed
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(2) +%28+.005a+%2B+.0075b+%29+%2F+250+=+.0065+
(2) +%28+.005%2A100+%2B+.0075%2A150+%29+%2F+250+=+.0065+
(2) +%28+.5+%2B+1.125+%29+%2F+250+=+.0065+
(2) +1.625+=+1.625+
OK