# Mathematical Foundations and Cost Options

“Mathematical literacy is an individual’s capacity to identify and understand the role that mathematics plays in the world, to make well-founded judgments, and to use and engage with mathematics in ways that meet the needs of that individual’s life as a constructive, concerned, and reflective citizen” (Mathematical Literacy, 2003). People face several situations in daily life that call for mathematical foundation for making informed decisions. The perception of mathematical concepts is however critical in solving various job problems and understanding of mathematical fundamentals (Mac-Lane & Birkhoff, 1999). Therefore, the real life scenario selected here is the first of the four options given in the listed scenarios.

In the real world scenario, the application of mathematical literacy will provide solutions through mathematical operations to overcome problematic situations in our daily life. A person could make judgment of situations in the most appropriate manner that capacitates him or her in identifying the most suitable choice. But choosing the most relevant one is quite difficult. For instance, consider the case of telephone plans that are available to a customer. There are various plans and services provided by a telephone company to suit the needs of a customer. The customer after selecting the service provider prior to their requirements will find it more difficult to select from the numerous options available. In such situations mathematical literacy will come to the help of the customer in selecting the apt service or plan that is economically advantageous or optimally benefitting. Therefore, the plans of a telephone company are conceived in relation to the calling needs of a customer during a month.

Assume that the calling needs for a hypothetical customer is around 800 minutes per month. The customer is provided with two different plans; namely, a telephone plan that costs \$30 per month and another one with \$50 per month. The former plan offers the customer with 300 minutes of free usage and thereafter charges \$0.25 per minute. The latter service plan also offers a maximum of 300 minutes as free and charges \$0.10 per minute for the extra. For obtaining the most economical plan, the present situation is converted into a mathematical form of y=mx+b. Let ‘y’ be the total amount that has been billed on the basis of the customer’s calling time and let ‘x’ be the extra minutes the customer uses after the free minutes. In the above equation ‘m’ denotes the extra charging rates per minute and ‘b’ denotes the charging rate for the selected service plan. So, the required algebraic equations for the above scenarios are as follows:

## \$30 per month plan

The calling requirements are taken as 800 minutes with 300 minutes as free usage. For every extra minute called, the customer has to pay \$0.25. Thus the defined variables will have the following values,

x = 800 – 300 = 500; b = 30; m = 0.25

y = 0.25 * x + 30

The customer is bound to pay \$155 billed against the total calling charges.

y = 0.25 x 500 + 30 = 155.

## \$50 per month plan

The calling requirement of the hypothetical customer is 800 minutes per month of which 300 minutes are free. For every extra minute called, the customer has to pay \$0.10.Thus, the defined variables will have the following values,

x = 800–300= 500; b= 50; m= 0.10

y = 0.10 * x + 50

Therefore, the customer will need to pay only the bill of \$100 towards calling for 800 minutes.

By comparing the above two results we take the two linear equations with the above two variables y and x.

y = 0.25 * x + 30…………….equation1

y = 0.10 * x + 50…………….equation2

By substitution method,

0.10 * x + 50= 0.25 * x + 30

x = 20/.15 = 133.33

y = 63.33

For the above values of ‘y’ and ‘x’ the lines denoting the two equations will intersect at a particular point. These equations will have the above values as the equivalent cost option.

Equation1:

• x = 300; y = 0.25*300+30 = 105
• x = 400; y =0.25*400+30 =130
• x = 500; y =0.25*500+30 =155

Equation2:

• x = 300; y = 0.10*300+50 =80
• x = 400; y =0.10*400+50 =90
• x = 500; y =0.10*500+50 =100

(X-axis: No. of extra minutes called; y-axis: Total amount billed)

The graph shows the difference in the amounts that are billed against the minutes called by the customer. From the above graphical representation and the equations, the best economical service plan that can be chosen for the customer is the 50\$ (fifty dollars) monthly plan.

## Conclusion

Mathematics is the logical analysis of various situations and its influence is seen in every aspect of our real life scenarios, including wealth. It is an operational language used and understood by all to solve the problems that encounter us. The basic knowledge of it will enhance fundamental calculations to plan and carry out income and expenditures sensibly. Mathematical literacy can provide befitting financial management as in the case of telephone services available for a customer. Through the mathematical applications, the customers can ideally choose any of the given satisfying and economical plans to suit their varying needs. An example towards this was elaborated as in the case of a customer who has been given two options in the form of a telephone plan that costs \$30 per month and another one with \$50 per month against the monthly calling needs. The first plan offered the customer with 300 minutes of free usage and thereafter charges \$0.25 per minute. The latter service plan also offered maximum 300 minutes as free and charges \$0.10 per minute. In order to obtain the most economical plan, the present situation was converted into mathematical equations and the results confirmed that the most economical plan for the customer was \$50.

Mathematics is heavily used in demographics, election data, opinion survey, economics, space technology, engineering, medicine, policy and decision making process, personal development, and hoards of other learning as well as working fields. It is therefore very important in life just like the knowledge of reading and writing (Lang, 2002). At present many people including students exhibit aversion to mathematics because of its complexities and sophistication. To remove such attitudes of the people more advanced but simplified learning procedures should be implemented by the authorities of academic institutions as well as governmental policy makers.

## References

Lang, S. (2002). Algebra. Reading, MA: Addison-Wesley.

Mac-Lane, S. & Birkhoff, G. (1999).Algebra. Reading, MA: Addison-Wesley.

Mathematical Literacy.(2003). OECD Programme for International Student Assessment (PISA). Web.

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