Answer:
Using the concept of linear equations, we find that we need 40 gallons of the 65% antifreeze and 10 gallons of the 90% antifreeze.
Step-by-step explanation:
Let x = amount of 20% antifreeze
Let y = amount of 70% antifreeze
Given that the total amount of antifreeze is 80 gallons
So, x + y = 80
Also given that the purity of the total antifreeze is 60%.
0.65x + 0.90y = 0.70(x + y)
65x + 90y = 70(x + y)
Simplify and solve the system of equations
65x + 90y = 70x + 70y
65x -70x+ 90y-70y = 0
-5x + 20y = 0
Now we have the following system of equations:
x + y = 50
-5x + 20y = 0
Multiply the first equation by 5 to get opposite coefficients for x;
add the equations to eliminate x
5x + 5y - 5x + 20y = 250
25y = 250
y = 10
Since the total mixed gallons is 50,
x = 50 - 10 = 40
So we need 40 gallons of the 65% antifreeze and 10 gallons of the 90% antifreeze
For more explanation, refer the following link:
https://brainly.com/question/8565372
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