Question

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.

Answer 1

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