Let x = the number of quarts of lubricant
Let y = the number of quarts of oil
Using these variables, we can write equations that represent the total number of quarts and total cost per quart of mixture.
x + y = 45 eq1
28x + 33y = 30 * 45 eq2
we multiply the right side of eq2 by total quarts in mixture to maintain equal units.
28x + 33y = 1350 eq2
We have a system of equations. The bold equations will be the equations to work with. To solve this system, we use the substitution method.
Substitute eq1 into eq2 so that eq2 is in terms of x.
28x + 33(45 - x) = 1350
Solve for x from this equation.
28x + 1485 - 33x = 1350
-5x = -135
x = 27
Substitute this value of x into eq1 to solve for y.
y = 45 - 27
y = 18
Number of quarts in lubricant is 27.
Number of quarts in oil is 18.
We are not done yet. Now, we have to convert quarts to volume.
Use the conversion factor:
1 quart = 57.75 cubic inches
So we multiply each quart by 57.75