Question

A scientist has a container of 2% acid solution and a container of 5% acid solution. How many fluid ounces of each concentration should be combined to make 25 fl oz of 3.2% acid solution?

Answer 1

Let 'a' be the number of ounces of 2%-solution in the 25-ounce mixture

and 'b' be the number of ounces of 5%-solution in the 25-ounce mixture.

Since, fluid ounces of each concentration should be combined to make 25 fl oz.

So, a+b=25 (Equation 1)

And, a container of 2% acid solution and a container of 5% acid solution should be combined to make 25 fl oz of 3.2% acid solution.

So, a of 2% + b of 5% = 3.2% of 25

$(a \times \frac{2}{100})+(b \times \frac{5}{100})= 25 \times \frac{3.2}{100}$

$(0.02a)+(0.05b)= 0.8$

Multiplying the above equation by 100, we get

$2a+5b=80$ (Equation 2)

Substituting the value of a=25-b in equation 2, we get

$2(25-b)+5b=80$

$50-2b+5b=80$

$50+3b=80$

$3b=30$

$b=10$

Since, a=25-b

a= 25-10

a=15.

So, 15 fluid ounces of 2% solution combined with 10 ounces of the 5% solution to create a 25-ounce mixture at 3.2% concentration of acid.