SOLUTION: Could someone please help me with this mixture problem? I have been pouring over it for two days (total of over 4 hours), and have tried various methods none of them yielding the

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Question 241234: Could someone please help me with this mixture problem? I have been pouring over it for two days (total of over 4 hours), and have tried various methods none of them yielding the correct answer.
A mechanic has 363 gallons of gasoline and 17 gallons of oil to make gas/oil mixtures. He wants one mixture to be 6% oil and the other mixture to be 2.5% oil. If he wants to use all of the gas and oil, how many gallons of gas and oil are in each of the resulting mixtures?
Answer by edjones(8007) (Show Source):
You can put this solution on YOUR website!
Let x=gals of gas required to make a .025 mixture.
Let y=gals of oil required to make a .025 mixture.
.
A) y/(x+y)=.025
B) (17-y)/(363-x+17-y)=.06
.
A)
y=.025x+.025y
.975y=.025x
y=.0256x
.
B)
(17-.0256x)/(380-x-.0256x)=.06
17-.0256x=22.8-.0615x
.0359x=5.8
x=161.56 gal
.
A)
y/(161.56+y)=.025
y=4.039+.025y
.975y=4.039
y=4.142 gal
It wont be exact because of rounding errors.
.
Ed