Use a system of equations to solve the following problem How

Use a system of equations to solve the following problem. How many ounces of a 12% alcohol solution and a 20% alcohol solution must be combined to obtain 48 ounces of a 16% solution?

oz of 12% alcohol solution =

oz of 20% alcohol solution =

Solution

If there are x ounces of 12%, then the rest (48 - x) is 20%.

So, just calculating the amount of alcohol in each part, and in the total, we have

0.12x + 0.20(48 - x) = 0.16*48

0.12x + 9.6 - 0.20x = 7.68

0.12x - 0.20x + 9.6 = 7.68

-0.08x + 9.6 = 7.68

-0.08x = 7.68 - 9.6

-0.08x = -1.92

cancel (-) sign:

0.08x = 1.92

x = 1.92/0.08

x = 24

Hence, oz of 12% alcohol solution = 24 ounce                        [ Answer ]

Now,

plug in the value of x in (48-x) , we get:

= 48 - 24

= 24

Hence, oz of 20% alcohol solution = 24 ounce                [ Answer ]