Having trouble setting up this math problem.

by Tyrell
(San Bernardino CA)

What is the percent strength (V/V) of alcohol in a mixture of 2000 ml of 35% (V/V) alcohol, 750ml of 55% (V/V) alcohol, and 750ml of 65% (V/V) alcohol?

Reply (by Keith)

In this case, what you have is 3 different solutions and you're probably 'pouring' them together into the same container. The best way to calculate the final strength is with an equation using basic algebra.

Here's how it will look:
We get the 3500 by adding up all of the volumes, and X is our unknown.
So, our mixture will equal 3500mL of and 'unknown' strength.

(2000)(.35)+(750)(.55)+(750)(.65)= (3500)(x)

Now, remember to follow P.E.M.D.A.S. order

P - Parenthesis

E - Exponents

M - Multiplication

D - Division

A - Addition

S - Subtraction

Which means multiplication before addition

Let's do it:

(2000)(.35)+(750)(.55)+(750)(.65)= (3500)(x)

700    +    412.5     +     487.50 = (3500)X

1600 = (3500)X

Now you must isolate X

1600        =          (3500)X

-------                --------
3500                    3500

X = .457

Move your decimal 2 spaces to the right to get the percent

The answer is 45.7%

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