You drive a car that runs on ethanol and gas. You have a 20-gallon tank to fill and you can buy fuel that it is either 25 percent ethanol or 85 percent ethanol. How much of each type of fuel should you buy to fill your tank so that it is 50 percent ethanol?

Can someone please help me?!?! This is solving for x & y. And it so complicated to me.! And worst of all I have a test on it tomorrow.! D:<

How did you figure out the value of x to = 35/3 (11.6666) gal of 25% ethanol??

To solve this problem, we need to determine the number of gallons of each type of fuel you should buy to achieve a 50 percent ethanol mixture in your 20-gallon tank.

Let's assume you need to buy x gallons of fuel that is 25 percent ethanol and y gallons of fuel that is 85 percent ethanol.

First, let's calculate the total amount of ethanol in each type of fuel:

1. Fuel with 25 percent ethanol: 0.25x gallons of ethanol
2. Fuel with 85 percent ethanol: 0.85y gallons of ethanol

Next, we'll calculate the total amount of ethanol in the tank when it's filled with these two types of fuel:

Total ethanol = (0.25x + 0.85y) gallons

Since you want to achieve a 50 percent ethanol mixture, the total ethanol must be half of the tank's capacity, which is 10 gallons (50 percent of 20 gallons).

So, we can write the following equation:

0.25x + 0.85y = 10

We also know that the total amount of fuel should be 20 gallons:

x + y = 20

Now, we have a system of two equations:

0.25x + 0.85y = 10
x + y = 20

To solve this system, we can use substitution or elimination.

Let's solve it using elimination:

Multiply the second equation by -0.25 to eliminate x:

-0.25(x + y) = -0.25(20)
-0.25x - 0.25y = -5

Now, add the two equations:

0.25x + 0.85y + (-0.25x - 0.25y) = 10 + (-5)
0.6y = 5

Divide both sides by 0.6:

y = 5 / 0.6
y ≈ 8.33

Substitute this value back into the second equation to find x:

x + 8.33 = 20
x ≈ 11.67

Therefore, you should buy approximately 11.67 gallons of fuel that is 25 percent ethanol and approximately 8.33 gallons of fuel that is 85 percent ethanol to fill your tank with a 50 percent ethanol mixture.

Let x=no. of gallons of 25% ethanol

then 20-x=number of gallons of 85%.
x*0.25 + (20-x)*0.85 = 20*0.5
Solve for x to get 35/3 gal. of 25% ethanol.

Thank you very much.(:

You're welcome!

t7u7i