Mixture Problem

Question

How many gallons of gasoline that is 8% ethanol must be added to 2,000 gallons of gasoline with no ethanol to get a mixture that is 6% ethanol?

Answer 1

Here,

       We have 2000 gallons of gasoline with no ethanol

       We want to add some 8% gasoline to make 6% gasoline

Let,

     gallons of gasoline that is 8% ethanol = x

(So the equation for the problem is going to be, Amount of current liquid * Percent of ethanol + Amount of liquid going to be added * Percent of ethanol = Total amount of liquid * Target amount of ethanol)

Lets solve the equation for x,

x*0.08+2000*0=(2000+x)*0.06

0.08x = 120 + 0.06x

0.08x - 0.06x = 120

0.02x = 120

x = 120/0.02

x = 6,000

Hence, 6,000 gallons of gasoline must be added

Answer 2

.08(X) +.00(2000) = .06(2000+X)

 

Solve this equation for X

 

 

The left side is the 2 parts separate

The right side is the mixture