Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 11 - Section 11.1 - Solving Quadratic Equations by Completing the Square - Exercise Set: 68

Answer

Rate of interest is r = 5%

Work Step by Step

Amount (A) = 882 Principal (P) = 800 Time (t) = 2 We have to find the rate of interest i.e. r. Step-1: Substitute the given values in the formula. $A=P(1+r)^t$ $882=800 (1+r)^2$ Step-2: We now solve the equation for r. $882=800 (1+r)^2$ Step-3: Divide both sides of the equation by 800 $\frac{882}{800}=(1+r)^2$ Step-4: Use the square root property $±\sqrt\frac{882}{800}=1+r$ Step-5: Simplify the left hand side by dividing the numerator and denominator by the Highest Common Factor(H.C.F) of 882 and 800 H.C.F of 882 and 800 is 2 $±\sqrt\frac{882\div2}{800\div2}=1+r$ $±\sqrt\frac{441}{400}=1+r$ $±\frac{21}{20}=1+r$ Step-6: Subtract both the sides with 1 and further simplify the left hand side $±\frac{21}{20}−1=r$ $±\frac{21-20}{20}=r$ Therefore,$ r=\frac{1}{20},\frac{−41}{20}$ Rate of Interest cannot be negative, hence, $r=\frac{1}{20}=0.05=$5%.
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