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Mathematical Problem Solving: Applications of Percentages, Logarithms, Permutations, and Financial Formulas

A comprehensive solution set for algebraic problems involving percentages, logarithms, and financial formulas.

Charlotte Kelly
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Mathematical Problem Solving: Applications of Percentages, Logarithms,Permutations, and Financial Formulas1.Acertain test is worth135points. How many points (roundedtothenearest point) are needed to obtain a score of85%?solution: total 135 points.pointsneeded to get 85% is:85/100X 135=114.75=115(approx)2.Inhow many ways can a chairperson and a vice chairperson beselected from a committee of25senators?solution:thereare 25 senators.wehaveto select 2 persons.sonumber of ways= 25 C 2=25!/(25-2)! x 2!=25!/23! X 2!=25x24/ 2=300ways answer3.Karenand Wayne need to buy a refrigerator because theirsjustbroke. Unfortunately, their savings account is depleted,andthey will need to borrow money in order to buy a new one.Searsoffers them an installment loan at14%(add-on rate). Iftherefrigerator at Sears costs$1,528plus 5% sales tax, andKarenand Wayne plan to pay for the refrigerator for 3 years,whatisthe monthly payment? (Round your answer to the nearestcent.)solution:Amountof refrigerator=1528salestax=5/100 x 1528=76.40sototal amount= 1528 + 76.40=1604.4letmonthlyinstalment= xrate=14%soi=14/1200=0.0116n=3years=36 monthsformula:Amount=x * (1+ i)^n-1/i *(1+i)^n1604.4=x * (1 + 0.0116)^ 36-1/0.0116 * (1+ 0.0116)^361604.4=x * (1.0116)^36-1/0.0116 * 1.0116^ 361604.4=x * 1.514-1/ 0.0116 * 1.5141604.4=x * 0.514/0.0059621604.4=x * 86.212

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