Question

in a lab, a 30% acid solution is being mixed with a 5% acid solution to create a 10% acid solution. what is the ratio of the amount of the 30% solution to the amount of 5% solution used to create the 10% solution?
1 : 6
1 : 4
1 : 3
1 : 5

Explanation:

Step1: Define variables

Let the amount of 30% solution be \( x \) and the amount of 5% solution be \( y \).

Step2: Set up the equation

The acid in the 30% solution is \( 0.3x \), the acid in the 5% solution is \( 0.05y \), and the acid in the 10% solution (total amount \( x + y \)) is \( 0.1(x + y) \). So, \( 0.3x + 0.05y = 0.1(x + y) \).

Step3: Simplify the equation

Expand the right side: \( 0.3x + 0.05y = 0.1x + 0.1y \). Subtract \( 0.1x \) and \( 0.05y \) from both sides: \( 0.2x = 0.05y \).

Step4: Find the ratio \( \frac{x}{y} \)

Rearrange the equation: \( \frac{x}{y} = \frac{0.05}{0.2} = \frac{1}{4} \).

Answer:

\( 1:4 \) (corresponding to the option "1 : 4")