Question

One antifreeze solution is 20% alcohol. Another antifreeze solution is 12% alcohol. How many liters of each solution should be combined to make 15 L of antifreeze solution that is 18% alcohol?

Answer 1

Use this systems of equations to solve:

x = first antifreeze
y = second antifreeze


`\left \{ {{.2x + .12y = .18(15)} \atop {x + y = 15}} \right.`

Isolate y.

x + y = 15
Subtract x from both sides.
y = -x + 15

Substitute y into the other equation.

.2x + .12(-x + 15) = .18(15)
Simplify.
.2x - .12x + 1.8 = 2.7
Subtract 1.8 from both sides.
.08x = .9
Divide both sides by .08
x = 11.25

Substitute x in the equation that we isolated y in.

y = -11.25 + 15
y = 3.75

11.25 L of the first antifreeze and 3.75 L of the second.