SOLUTION: Given 98% gasoline and 2% motor oil. New engine is 96% gasoline and 4% oil. write an equation in standard form that ma
kes the possible combination of each kind of mixture you ca
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Question 1204426: Given 98% gasoline and 2% motor oil. New engine is 96% gasoline and 4% oil. write an equation in standard form that ma
kes the possible combination of each kind of mixture you can prepare using 6 gallons of gasoline.
Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
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Given 98% gasoline and 2% motor oil. New engine is 96% gasoline and 4% oil. write an equation in standard form that ma,...
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Some basic language development is needed before you have a meaningful math application question.
A good guess is you have two mixtures. One is 98% gasoline and the other is 96% gasoline. You want to make an equation for 6 gallon gasoline using ...
the amount of mixture-final and the amount of the oil(the carrier?) are to be the variables.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
number of galons of gas = 6
number of gallons of oil = x
ratio of gas to total = y
i get x = 6/y - 6
when y = .98, the equation becomes x = 6/.98 - 6 which gets you x = .1224489796.
when y = .96, the equation becomes x = 6/96 - 6 which gets you x = .25.
if 6 gallons of gas is 98% of the total, then the number of gallons of oil is equal to .1224489796.
if 6 gallons of gas is 96% of the total, then the number of gallons of oil is equal to .25.
at 98% gas, the total is 6.1224489796 gallons.
6 divided by that = .98
.12244489796 divided by that = .02
at 6% gas, the total is 6.25 gallons.
6 divided by that = .96
.25 divided by that = .04
the general equation for the number of gallons of oil required if you have 6 gallons of gas is x = 6/y - 6.
x is the number of gallons of oil required.
y is the ratio of gallons of gas to the total mixture.
the total mixture is expressed as 6/y.
x is the nmber of gallons of oil required.
the total mixture is expresed by the equation 6/y = 6 + x.
y is the ratio of gallons of gas to total gallons of mixture.
x is the number of gallons of oil reuired.
since x = 6/y - 6, you can replace x with that to get:
6/y = 6 + 6/y - 6
you wind up with 6/y = 6/y which is correct.
what i wind up with is:
standard form equation is 6y + xy = 6
x is the number of gallons of oil required.
y is the ratio of gallons of gas to total number of gallons.
it's a litle complex, but it works.
when y = .98, the equation becomes 6 * .98 + x * .98 = 6
simplify to get 5.88 + .98 * x = 6
subtract 5.88 from both sides of the equation to get .98 * x = .12
solve for x to get x = .12 /.98 = .1224489796.
this is the correct answer as we derived above when 6 = .98 of the total mixture.
when y = .96, the equataion becomes 6 * .96 + x * .96 = 6
simplify to get 5.76 + .96 * x = 6
subtract 5.76 from both sides of the equation to get .96 * x = .24
solve for x to get x = .24 / .96 = .25.
this is the correct answer as we derived above when y = .96 of the total mixture.
it's important to know exactly what x and y represent.
the equation is 6 * y + x * y = 6
y is the ratio of gallons of gas to total gallons of mixture.
x is the number of gallons of gas.
with this equation, you can figure out how many gallons of oil you need to make any mixture with 6 gallons of gas.
all you need to do is provide the ratio of gallons gas to total gallons of mixture.
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