Question

A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 35% salt and Solution B Is 65%salt. She wants to obtain 120 ounces of a mixture that is 40 % salt. How many ounces of each solution should she use?Solution A:Solution B:

Answer 1

Given: Solution A is 35% salt and Solution B Is 65% salt

To Determine: How many ounces of each solutions A and B

Solution

Let the number of ounces for solution A be x, and the number of ounces for solution B be y

Since the total number of ounces is 120, then our first equation is

$equation1:x+y=120$

Since we have the percentage of salt in solution A and solution B, and the mixture, then the second equation would be

$\begin{gathered} equation2:35\%\times x+65\%\times y=40\%\times120 \\ equation2:0.35x+0.65y=48 \end{gathered}$

Let us compare the two equations together as shown below

$\begin{gathered} equation1:x+y=120 \\ equation2:0.35x+0.65y=48 \\ from:equation1 \\ y=120-x \end{gathered}$

Substitute y intoequation 2

$\begin{gathered} 0.35x+0.65(120-x)=48 \\ 0.35x+78-0.65x=48 \\ 0.35x-0.65x=48-78 \\ -0.3x=-30 \\ x=\frac{-30}{-0.3} \\ x=100 \end{gathered}$

Let us substitute x into y

$\begin{gathered} y=120-x \\ y=120-100 \\ y=20 \end{gathered}$

Hence, the ounces used for each solution would be

Solution A : 100 ounces

Solution B : 20 ounces