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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.

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    Mathematical Problem Solving: Applications of Percentages, Logarithms, Permutations, and Financial Formulas 1.A certain test is worth 135 points. How many points (rounded to the nearest point) are needed to obtain a score of 85% ? solution: total 135 points. points needed to get 85% is: 85/100 X 135 = 114.75 = 115 (approx) 2.In how many ways can a chairperson and a vice chairperson be selected from a committee of 25 senators? solution: there are 25 senators. we have to select 2 persons. so number of ways= 25 C 2 = 25!/(25 - 2)! x 2! =25!/ 23! X 2! =25 x 24/ 2 =300 ways answer 3.Karen and Wayne need to buy a refrigerator because theirs just broke. Unfortunately, their savings account is depleted, and they will need to borrow money in order to buy a new one. Sears offers them an installment loan at 14% (add - on rate). If the refrigerator at Sears costs $1,528 plus 5% sales tax, and Karen and Wayne plan to pay for the refrigerator for 3 years, what is the monthly payment? (Round your answer to the nearest cent.) solution: Amount of refrigerator=1528 sales tax=5/100 x 1528=76.40 so total amount= 1528 + 76.40 =1604.4 let monthly instalment= x rate=14 % so i= 14/1200=0.0116 n= 3 years=36 months formula: Amount=x * (1+ i)^n - 1/i *(1+i)^n 1604.4= x * (1 + 0.0116)^ 36 - 1/0.0116 * (1+ 0.0116)^36 1604.4=x * (1.0116)^36 - 1/0.0116 * 1.0116^ 36 1604.4=x * 1.514 - 1/ 0.0116 * 1.514 1604.4=x * 0.514/0.005962 1604.4= x * 86.212

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    or x=1604.4/86.212 x=18.6 answer 4.Suppose that an insurance agent offers you a policy that will provide you with a yearly income of $30,000 in 30 years. What is the comparable salary today, assuming an inflation rate of 5% compounded annually? (Round your answer to the nearest cent.) solution: A =30000 * (1+i)^ - n A=30000 / (1+i)^n A=30000 / (1+.05)^30 A=30000/4.3219 A=6940 answer 5.Evaluate the given expressions (to two decimal places). a.log 17.9 = log (179/10) = log( 27 x 7/10) = log 27 + log 7 - log 10 =3 log 3 + log7 - log 10 = 3 x 0.477 + 0.845 - 1 = 1.431 + 0.845 - 1 = 1.276 answer b.log2 512 log2 2^9 = 9 x log2 2 =9 x1 =9 answer c.log2 1 d.log0.042 = log (42/1000) = log(7x6 /1000) = log 7 + log6 - log 1000 =0.845 + 0.778 - 3 log 10 =1.623 - 3 = - 1.376 answer 6.Solve each exponential equation. Give the exact value for x .(The x's look like small exponent x's in the problem) a.1.7x=1/49 b.2.5x=8 c.6x=4.5

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