SOLUTION: A mechanic has 340 gallons of gasoline and 10 gallons of oil to make gas/oil mixtures. He wants one mixture to be 4% oil and the other mixture to be 2.5% oil. If he wants to use al
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Question 488190: A mechanic has 340 gallons of gasoline and 10 gallons of oil to make gas/oil mixtures. He wants one mixture to be 4% 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 josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = total gallons of gas + oil in the 4% oil mixture
Let = total gallons of gas + oil in the 2.5% oil mixture
-----------
given:
The % of gas in the 4% oil mixture is 96%
The % of gas in the 2.5% oil mixture is 97.5%
total gallons of gas + oil in the 2 mixtures
(1)
(2)
(3)
------------------------
Multiply both sides of (2) and (3) by
(1)
(2)
(3)
------------------------
Multiply both sides of (3) by
and subtract (2) from (3)
(3)
(2)
and, since
(1)
(1)
(1)
-----------------
gallons
gallons
and
gallons
------------------------
There are 80 gallons of gas in the 4% oil mixture
There are 3 and 1/3 gallons of oil in the 4% oil mixture
------------------------
There are 260 gallons of gas in the 2.5% oil mixture
There are 6 and 2/3 gallons of oil in the 2.5% oil mixture
------------------------
check:
OK
and
and
OK
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