SOLUTION: A new automobile engine can run on a mixture of gasoline and a substitute fuel. If gas costs $1.50 per gallon and the substitute fuel costs 40 cents per gallon, what percent of a m

Question 104438This question is from textbook College Algebra
: A new automobile engine can run on a mixture of gasoline and a substitute fuel. If gas costs $1.50 per gallon and the substitute fuel costs 40 cents per gallon, what percent of a mixture must be substitute fuel to bring the cost down to $1.00 per gallon? This question is from textbook College Algebra

Answer by stormy(4) (Show Source): You can put this solution on YOUR website!
Let g = the number of gallons of gas and s = the number of gallons of substitute fuel in the mixture. Then:

The price of g gallons of gas = 1.50 g
The price of s gallons of substitute fuel = 0.40 s

Therefore, the price of the mixture is: 1.50 g + 0.40 s

To get a price of 1.00 per gallon, you have to mix the two types. The price of this mixture is $1 multiplied the total number of gallons in the mixture:

1.00 ( g + s )

Now set the two expressions for the price of the mixture equal to each other and solve for "g":

1.50 g + 0.40 s = 1.00 ( g + s )
1.50 g + 0.40 s = 1.00 g + 1.00 s
1.50 g - 1.00 g = 1.00 s - 0.40 s
0.50 g = 0.60 s
g = (0.60 / 0.50) s
g = 1.2 s

From this we see that we need 1.2 gallons of gas for every gallon of substitute fuel.

We can now calculate the percentage of substitute fuel in the mixture:

s / (g + s) = s / (1.2s + s) = s / 2.2s = 0.4545, or 45.45%

To check our solution, verify that 45.45% of the substitute fuel price added to 100 - 45.45 = 54.55% of the gas price equals $1.00:

0.5455($1.50) + 0.4545($0.40) = $1.00

It does!
RELATED QUESTIONS
A new automobile engine can run on a mixture of gasoline and a substitute fuel. If gas... (answered by scott8148)

A new automobile engine can run on a mixture of gasoline and a substitute fuel. If gas... (answered by josgarithmetic)

A new automobile engine can run on a mixture of gasoline and a substitute fuel. If gas... (answered by josmiceli)

An automobile engine can run on a mixture of gasoline and a substitute fuel. If gas costs (answered by ankor@dixie-net.com)

an automobile engine can run on a mixture of gasoline and a substitute fuel. if gas costs (answered by stanbon)

44. A new automobile engine can run on a mixture of gasoline and a substitue fuel. If gas (answered by ankor@dixie-net.com)

Henry Ford�s Model T was originally designed and built to be run on ethanol. Today... (answered by Theo)

A boat owner mixes together oil and gasoline to make 40 gallons of fuel for his boat. The (answered by twinzmom)

(1 pt) Suppose a fuel mixture is 2% ethanol and 98% gasoline. How much ethanol (in... (answered by josmiceli)