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Solving a percent mixture problem using a system of linear..EspanolA scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 70% salt and Solution B is 95%salt. She wants to obtain 90 ounces of a mixture that is 85% salt. How many ounces of each solution should she use?Note that the ALEKS graphing calculator can be used to make computations easier.

Solving a percent mixture problem using a system of linear..EspanolA scientist has-example-1
User Longda
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1 Answer

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Final mixture: 90oz of 85% salt:

Find the 85% of 90 to know the ounces of salt in the final mixture:


90\cdot0.85=76.5oz\text{ salt}

If A is the ounces of solution A and B the ounces of solution B, the sum of A and B is equal to 90oz:


A+B=90

The quantity of salt in solution A is 0.7A, the quantity of salt in solution B is 0.95B. The sum of 0.7A and 0.95B needs to be 76.5 (Total quantity of slat in the final mixture):


0.7A+0.95B=76.5

______

Use the next system of linear equations to find A and B:


\begin{gathered} A+B=90 \\ 0.7A+0.95B=76.5 \end{gathered}

1. Solve A in the first equation:


A=90-B

2. Substitutet he A in the second equation by the value you get in step 1:


0.7(90-B)+0.95B=76.5

3. Solve B:


\begin{gathered} 63-0.7B+0.95B=76.5 \\ 63+0.25B=76.5 \\ \text{0}.25B=76.5-63 \\ 0.25B=13.5 \\ B=(13.5)/(0.25) \\ \\ B=54 \end{gathered}

4. Use the value of B to find A:


\begin{gathered} A=90-B \\ A=90-54 \\ A=36 \end{gathered}Then, to get a final mixture of 90oz of 85% salt you use 36 ounces of solution A and 45 ounces of solution B
User Nishant Lakhara
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