Question 345966
We have to figure out what mixture of pure antifreeze must be mixed with 40% antifreeze to give a 60% soln

let x be the amount of 40% (.4) soln and 6-x be the amount of 100% (1) antifreeze.
In 6 quarts of 60% antifreeze is 3.6 quarts of pure antifreeze.
0.4x+6-x=3.6

Since 0.4x and -x are like terms, add -x to 0.4x to get -0.6x.
-0.6x+6=3.6

Since 6 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 6 from both sides.
-0.6x=-6+3.6

Add 3.6 to -6 to get -2.4.
-0.6x=-2.4

Divide each term in the equation by -0.6.
-(0.6x)/(-0.6)=-(2.4)/(-0.6)

Cancel the common factor of -0.6.
x=-(2.4)/(-0.6)

Simplify the right-hand side of the equation by simplifying each term.
x=4