Question

a chemist creates 180 milliliters of a 42.5% alcohol solution by combining a 15% alcohol solution with a 70% alcohol solution. if x represents the amount of the 15% alcohol solution used and y represents the amount of the 70% alcohol solution used, which of the following could be used to model the given information?
{ x + y = 180
0.015x + 0.07y = 76.5
{ x + y = 180
15x + 70y = 42.5
{ x + y = 180
0.15x + 0.7y = 42.5
{ x + y = 180
0.15x + 0.7y = 76.5
{ x + y = 180
1.5x + 7y = 76.5

Explanation:

Step1: Analyze the total volume equation

The total volume of the final solution is 180 milliliters. Since \(x\) is the volume of the 15% solution and \(y\) is the volume of the 70% solution, we have \(x + y=180\).

Step2: Analyze the alcohol - content equation

The amount of alcohol in the 15% solution is \(0.15x\) (because 15%=\(0.15\)), the amount of alcohol in the 70% solution is \(0.7y\) (because 70%=\(0.7\)), and the amount of alcohol in the final 42.5% solution of 180 milliliters is \(0.425\times180 = 76.5\). So, \(0.15x+0.7y = 76.5\).

Answer:

\(

$$\begin{cases}x + y=180\\0.15x + 0.7y=76.5\end{cases}$$

\)