SOLUTION: A petroleum company has two different sources of crude oil. The first source provides crude oil that is 25% hydrocarbons, and the second one provides crude oil that is 75% hydrocar

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Question 1025535: A petroleum company has two different sources of crude oil. The first source provides crude oil that is 25% hydrocarbons, and the second one provides crude oil that is 75% hydrocarbons. In order to obtain 80 gallons of crude oil that is 65% hydrocarbons, how many gallons of crude oil must be used from each of the two sources?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = gallons of 25% crude needed
Let +b+ = gallons of 75% crude needed
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(1) +a+%2B+b+=+80+
(2) +%28+.25a+%2B+.75b+%29+%2F+80+=+.65+
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(2) +.25a+%2B+.75b+=+.65%2A80+
(2) +.25a+%2B+.75b+=+52+
(2) +25a+%2B+75b+=+5200+
(2) +a+%2B+3b+=+208+
Subtract (1) from (2)
(2) +a+%2B+3b+=+208+
(1) +-a+-+b+=+-80+
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+2b+=+128+
+b+=+64+
and
(1) +a+%2B+b+=+80+
(1) +a+=+16+
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16 gallons of 25% crude is needed
64 gallons of 75% crude is needed
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check:
(2) +%28+.25%2A16+%2B+.75%2A64+%29+%2F+80+=+.65+
(2) +%28+4+%2B+48+%29+%2F+80+=+.65+
(2) +52%2F80+=+.65+
(2) +52+=+.65%2A80+
(2) +52+=+52+
OK