SOLUTION: A mechanic has 341 gallons of gasoline and 18 gallons of oil to make gas/oil mixtures. He wants one mixture to be 8% oil and the other mixture to be 3.5% oil. If he wants to use al

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Question 545041: A mechanic has 341 gallons of gasoline and 18 gallons of oil to make gas/oil mixtures. He wants one mixture to be 8% oil and the other mixture to be 3.5% 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?
i know that:
mixture A = oil/(oil+gas)=.08
mixture B = oil/(oil+gas)=.035
if i mix all the gas and oil together i get a 5.013% soulution.
it's supposed to be a system of equations problem.. but my answer document has four blanks to fill in because there are two mixtures, but i cannot figure out how i would even go about this problem.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A mechanic has 341 gallons of gasoline and 18 gallons of oil to make gas/oil mixtures.
He wants one mixture to be 8% oil and the other mixture to be 3.5% 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?
:
let a = amt of mixture which is 8% oil
let b = amt of mixture which is 3.5% oil
:
The oil equation
.08a + .035b = 18
the gas equation
.92a + .965b = 341
:
Multiply the 1st equation by 23, multiply the 2nd equation by 2
1.84a + .805b = 414
1.84a + 1.93b = 682
---------------------subtraction eliminates a, find b
-1.125b = -268
b =
b = +238.2 gal of the 3.5% mixture
then
.035(238.2) = 8.337 gal of oil in the 3.5% mixture
and
.965(238.2) = 229.863 gal of gas int he 3.5% mixture
:
How about the 8% mixture?
18 - 8.337 = 9.663 gal of oil in the 8% mixture
and
341 - 229.863 = 111.137 gal of gas in the 8% mixture