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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:

User Xmnboy
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1 Answer

11 votes
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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\%* x+65\%* y=40\%*120 \\ 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=(-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

User A Rogue Otaku
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