this term you have learned how to model the solution to a problem using algebra. Once we know how to create the equations, we have the means of solving **all** problems of a given type.

Please submit your final project here. Remember to show all of your work here so partial credit can be given if there are errors. Post a summary of your topic to the Week 7 discussion board. Review the topic you chose in the Week 6 Proposal. Also, review the rubric before submitting.

For the final project please do all of the following steps:

- Restate your scenario and the specific data you are using. This topic was approved in the Week 6 Proposal. Be sure to cite any sources if you use outside references for ideas or data.
- Write a linear equation of the form y1 = mx + b for your first set of data. Graph this equation on the xy-plane and label it as y1. You may use Excel to graph, search online for graph paper options to use, or use the ‘draw’ tools in Word to plot your lines Graphsketch.com is resource which you may find helpful when constructing your graph. Also, be sure to include a title on the graph and labels on the x- and y-axes.
- Write a linear equation of the form y2 = mx + b for the other equation in your system. Graph this equation on the same graph. You will now have two lines on the same graph. These should intersect.
- Find the point of intersection for y1 and y2 algebraically (by setting the equations equal to each other and solving). Show your work and also plot this point on the graph.
- Analyze the data and explain what the intersection means, in terms of the problem. Is there a ‘best’ solution to your problem? If so, under what conditions?
- Conclude your project with a short summary of what you learned.

Final Project Proposal

PROBLEM STATEMENT

Chemicals such as trichloroacetic acid, glycolic acid, salicylic acid, etc. are key

ingredients of skin-care products and are also found in various medicines used by dermatologists

for treating skin infections. The concentration of these chemicals differs from product to

product. While manufacturing any of these products, we may require a specific concentration of

the chemical solution to mix with other ingredients. Unfortunately, finding a specific

concentration is not an easy task, and it may not be available on the market, as most chemicals

come with standard concentrations. Sometimes it requires additional preparations, such as

diluting the concentrated solution or mixing two different concentrations of the chemical to

create the desired concentration of the chemical solution.

Objective:

Finding the mixing volumes of two solutions of different concentrations of a chemical to

make the desired concentration of the solution.

Description:

While mixing two different concentrated solutions to create the desired concentration of

the chemical, we can use a system of linear equations to model the problem and find the correct

mixing volume of the two solutions. Suppose I work as a chemist in a pharma industry that

requires 15 liters of 50% glycolic acid to manufacture 1000 units of a skin care product. After

researching the market, I found an online website that sells 30% and 70% glycolic acid solutions.

Shopping website: https://www.laballey.com/pages/search-results-page?q=glycolic%20acid

For modeling the two equations, as we will have two unknowns (volume of 30% solution and

volume of 70% solution), we will consider these two facts:

1. Vol of 30% Solution + Vol of 70% Solution = 15

2. Chemical content in 30% solution + in 70% solution = Chemical content in mixture

I intend to formulate and solve these two equations to find the desired mixing volume of the two

solutions.