Question 1204426
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.