Solving proportions Essay Example for Free

Solving proportions EssayProportions exist in many real-world applications, and in this problemestimating the size of the bear community on the Keweenaw Peninsula. By comparingdata from two experiments, conservationists are able to predict patterns of animalincrease or decrease. In this situation, 50 bears were captured and labeled and released to visualise the size of the bear population. A year later, after capturing a random sample of100 bears only 2 of the bears captured were tagged bears. These proportions will be employto determine the bear population on the peninsula. This new bear scenario can be lickby applying the concept of proportions which allows the assumption of the symmetry oforiginally tagged bears to the whole population is equal to the ratio of recaptured taggedbears to the size of the sample. To determine the estimated solution, the bears will be theextraneous variables that will be defined for solving the proportions used.The ratio of originally tagged b ears to the whole population X_2_The ratio of recaptured tagged bears to the sample size 10050 = _2_ This is the proportion set up and ready to solve. X 100(50)(100), (X)(2)The conterminous step is to cross multiply.5000 = 2X Divide both sides by 22 22500 = XThe bear population on the Keweenaw Peninsula is estimated to bearound 2500.The extreme center for this sample were 50 and 100, X and 2.For the second problem in this assignment, the par must be solved for Y.Continuing the discussion of proportions, a single figure (ratio) exists on both sidesof the equal sign so basically it is a proportion, which can be solved bycrossmultiplying the extremes and means.Y-1 = 3 Original comparability solving for YX+3 44(Y-1) = -3(X+3) Cross multiply both sides4Y-4 = -3X-9 Add 4 to both sides4Y = -3X-5 Divide both sides by 4Y = -3X-5 Final answer for Y4 4This is a linear equation in the form of y = mx + b. After comparing the solutionto the original problem, it is noticed that the slope, -3 /4 ,is the same number on the rightside of the equation. This indicates that another method exists for solving the sameequation.Y-1 = 3 Original equation solving for YX+3 4Y-1 = -3(X+3) Multiply both sides by (X+3)4Y-1 = -3X-9 Add 1 to both sides4 4Y = -3X-5 Final answer4 4After solving both of these problems I found it interesting how 2 totally differentequations could be solved with the same basic functions. I also found that everyday keepcan incorporate these math functions to solve or estimate daily life events for a number ofdifferent reasons..REFERENCESReferences Elementary and Intermediate Algebra, 4th Ed., Dugopolski