Problema Solution
You drive a car that runs on ethanol and gas. You have a 20 gallon tank to fill and you can buy fuel that is either 25 percent ethanol or 85 percent ethanol. How much of each type of fuel should tou buy to fill your tank so it is 50 percent ethanol?
Answer provided by our tutors
Let
x = gallons of the 25% ethanol fuel
y = gallons of the 85% ethanol fuel
We can write the following
the total of both fuels in the tank
x + y = 20
25% ethanol of the first fuel + 85% ethanol of the second fuel should give 50% of the total
0.25*x + 0.85*y = 0.50*(x+y)
By solving the system
x + y = 20
0.25*x + 0.85*y = 0.50*(x+y)
we find that
x = 11.67 gallons
y = 8.33 gallons
We need 11.67 gallons of the 25% ethanol fuel and 8.33 gallons of the 85% ethanol fuel so that our tank has 50% ethanol fuel in it.