Algebra

Solution: Let x = the quantity of Arabica(M) (in kg) and y = quantity of Robusta(H) (in kg) Based on the given information, equations may be set up as: 10.50(x) + 9.25(y) = (9.74)(2500) ---? equation (1) x + y = 2500 ---? equation (2) Graphing each equation on the same xy-plane: By applying substitution method (equation (2) into equation (1)): 10.50(x) + 9.25*(2500 – x) = (9.74)(2500) 10.50(x) + 23125 - 9.25(x) = 24350 1.25(x) = 1225 Then dividing each side by 0.8, x = 980 kgs Arabica(M) And 980 + y = 2500 ---? y = 1520 kgs Robusta(H) Thus, the point of intersection is at (980, 1520) and this pertains to the quantities each of the Arabica(M) and the Robusta(H) that must be present in the bean-mixture so that Matthew is able to satisfy the condition of selling a total of 2500-kg mixture where each kilogram is sold for $9.74. Summary of Learning Besides its flexible range of applications, I have learned that there can be alternative methods in solving a system of equations once each equation has been properly set up with correct algebraic expressions in which variables are made to represent unknown amounts of objects either count or non-count by nature. I appreciate the fact that in Algebra, one is able to verify the existence of a solution by using methods of elimination and substitution wherein one method can be a means to countercheck the other which ought to show the same results. It is quite interesting that equations may be graphed to determine whether real solutions exist as via intersection of lines. Having become acquainted with different function types such as linear, polynomial, rational, logarithmic, and exponential, I gain knowledge of constructing relations among dependent and independent variables as well as arbitrary constants based on useful empirical data. Summary of Topic In the model mixture problem, businessmen like Matthew can set constraints in terms of cost, quantity of material or commodity under consideration, selling price, and additional concerns that may possibly be incorporated in formulating labels and pertinent equations. Normally, problems of such kind possess linear relationships of variables for which the number of solutions rely on the highest degree of independent variable by which to identify the number of intersection points between the set of equations involved. Alternative Project In its existence and approach, Algebra serves as a base device to higher math such as Calculus which attempts to explore the grounds for the undefined nature of a function and designates a sensible understanding about up to which extent it would exist considering assumptions or applicable conditions. Fundamentals of algebra are essential to the foundation of courses designed to solve multivariable systems through linear programming, matrix applications, and differential equations where there is ceaseless necessity for equations and functions in interpreting problem situations. They are especially of ample advantage as tools for working chemists and biochemists who deal with cases of radioactive decomposition or rates of reactions for instance. Hence, chemical studies under such field may include the use of exponential function A = A0*e-kt where ‘A’ stands for the element concentration or amount at any time ‘t’
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