Suppose you have two alcohol+water solutions. One solution ( of volume x liter ) is 45% alcohol, while the second solution (of volume y liter) is 75% alcohol. What values of "x" and "y" (in liters) will fill a total volume of 5.0 liter which contains 2.88 liters of alcohol ?
I need to make two equations from this and use the substitution or elimination method to solve this problem.
x + y = 5.0
0.45 x + 0.75 y = 2.88
Now you do the algebra.
x=2.9
y=2.1
Let's create two equations based on the given information:
Equation 1: The sum of the volumes of the two solutions equals 5 liters:
x + y = 5 (Equation 1)
Equation 2: The sum of the volumes of alcohol from each solution equals 2.88 liters:
0.45x + 0.75y = 2.88 (Equation 2)
Now, we have a system of two equations. We can solve this system using substitution or elimination method.
Let's solve it using the substitution method.
From Equation 1, we get:
x = 5 - y
Now, substitute this value of x into Equation 2:
0.45(5 - y) + 0.75y = 2.88
2.25 - 0.45y + 0.75y = 2.88
0.30y = 2.88 - 2.25
0.30y = 0.63
Now, solve for y:
y = 0.63 / 0.30
y ≈ 2.1 liters
Substitute the value of y back into Equation 1 to find x:
x + 2.1 = 5
x = 5 - 2.1
x ≈ 2.9 liters
Therefore, the values of x and y are approximately 2.9 liters and 2.1 liters, respectively, to fill a total volume of 5.0 liters containing 2.88 liters of alcohol.
To solve this problem using the substitution or elimination method, we need to set up two equations based on the given information. Let's denote the volume of the first solution as "x" liters and the volume of the second solution as "y" liters.
1. The equation for the total volume:
x + y = 5.0
2. The equation for the total amount of alcohol:
0.45x + 0.75y = 2.88
Now, we can use either the substitution or elimination method to solve these equations. Let's use the substitution method.
From the first equation (x + y = 5.0), we can express x in terms of y as:
x = 5.0 - y
Now, substitute this expression for x in the second equation (0.45x + 0.75y = 2.88):
0.45(5.0 - y) + 0.75y = 2.88
Simplify and solve this equation to find the value of y:
2.25 - 0.45y + 0.75y = 2.88
0.3y = 0.63
y = 0.63 / 0.3
y ≈ 2.1
Now, substitute this value of y back into the first equation (x + y = 5.0) to find the value of x:
x + 2.1 = 5.0
x ≈ 5.0 - 2.1
x ≈ 2.9
Therefore, the values of x and y that will fill a total volume of 5.0 liters, which contains 2.88 liters of alcohol, are approximately x = 2.9 liters and y = 2.1 liters.