A 21% oil gas mixture is to be formed by mixing 80% and 20% oil_gas mixtures. If 35L are required l, how much of each should be used?
Well, let's think about it. We need to make a 21% oil gas mixture using 80% and 20% oil gas mixtures.
So, if we let x represent the amount of 80% mixture used and y represent the amount of 20% mixture used, we can set up a system of equations.
First, we know that the total volume of the mixture should be 35L, so we have the equation x + y = 35.
Second, we know that the amount of oil gas in the mixture should be 21% of the total volume, which means 0.21 * 35 = 0.21x + 0.21y.
So, we have the system of equations:
x + y = 35
0.21x + 0.21y = 0.21 * 35
Now, solving this system of equations would give us the amounts of each mixture to use. But since I'm a Clown Bot and not a math bot, I'll just entertain you with a joke instead:
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Because they make up everything!
To solve this problem, we can set up an equation based on the amount of pure oil and pure gas needed in the final mixture.
Let's assume x liters of the 80% oil_gas mixture is used and y liters of the 20% oil_gas mixture is used.
The amount of oil in x liters of 80% oil_gas mixture is 0.8x liters, and the amount of oil in y liters of 20% oil_gas mixture is 0.2y liters.
The total oil in the final mixture should be 21% of 35 liters, which is 0.21 * 35 = 7.35 liters.
Setting up the equation for oil:
0.8x + 0.2y = 7.35 (equation 1)
The total gas in the final mixture should also be 21% of 35 liters, which is 0.21 * 35 = 7.35 liters.
Setting up the equation for gas:
0.2x + 0.8y = 7.35 (equation 2)
Now we have a system of equations:
0.8x + 0.2y = 7.35 (equation 1)
0.2x + 0.8y = 7.35 (equation 2)
To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of elimination:
Multiply equation 1 by 4:
3.2x + 0.8y = 29.4 (equation 3)
Subtract equation 3 from equation 2:
(0.2x + 0.8y) - (3.2x + 0.8y) = 7.35 - 29.4
-3x = -22.05
Divide both sides by -3:
x = 7.35
Now substitute the value of x back into equation 1:
0.8(7.35) + 0.2y = 7.35
5.88 + 0.2y = 7.35
0.2y = 7.35 - 5.88
0.2y = 1.47
y = 1.47 / 0.2
y = 7.35
Therefore, to form a 21% oil_gas mixture using 35 liters, 7.35 liters of the 80% oil_gas mixture and 7.35 liters of the 20% oil_gas mixture should be used.
To solve this problem, we need to set up an equation based on the given information.
Let's assume that we need to use x liters of the 80% oil_gas mixture and y liters of the 20% oil_gas mixture.
Since the resulting mixture is to be 35 liters, we can set up the equation:
x + y = 35 --- Equation 1
Now let's consider the oil content in the mixture.
The 80% oil_gas mixture is comprised of 80% oil and 20% gas, and the 20% oil_gas mixture is made up of 20% oil and 80% gas.
We want to create a 21% oil_gas mixture, which means the resulting mixture will contain 21% oil and 79% gas.
To find the oil content in the resulting mixture, we can set up the equation:
(0.80x + 0.20y) / 35 = 0.21
Simplifying this equation:
0.80x + 0.20y = 0.21 * 35
0.80x + 0.20y = 7.35 --- Equation 2
We now have a system of equations with Equation 1 and Equation 2. We can solve this system to find the values of x (amount of the 80% oil_gas mixture) and y (amount of the 20% oil_gas mixture).
Solving the system of equations:
Equation 1: x + y = 35
Equation 2: 0.80x + 0.20y = 7.35
One way to solve this system is by using the substitution method. We can solve Equation 1 for x and substitute it into Equation 2:
x = 35 - y
Substituting x = 35 - y into Equation 2:
0.80(35 - y) + 0.20y = 7.35
28 - 0.80y + 0.20y = 7.35
-0.60y = 7.35 - 28
-0.60y = -20.65
Dividing both sides by -0.60:
y = 20.65 / 0.60
y ≈ 34.42
Now, we can substitute the value of y back into equation 1 to solve for x:
x + 34.42 = 35
x ≈ 0.58
Therefore, to create a 21% oil_gas mixture of 35 liters, you should mix approximately 0.58 liters of the 80% oil_gas mixture and 34.42 liters of the 20% oil_gas mixture.
Oil = 0.8 * 35.
Gas = 0.2 * 35.