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: 70

Answer

Rate of Interest = 20%

Work Step by Step

Amount (A) = 2880 Principal (P) = 2000 Time (t) = 2 We have to find the rate of interest i.e. r. Step-1: Substitute the given values in the formula. $A=P(1+r)^t$ $2880=2000 (1+r)^2$ Step-2: We now solve the equation for r. $2880=2000 (1+r)^2$ Step-3: Divide both sides of the equation by 2000 $\frac{2880}{2000}=(1+r)^2$ Step-4: Use the square root property $±\sqrt\frac{2880}{2000}=1+r$ Step-5: Simplify the left hand side by dividing the numerator and denominator by the Highest Common Factor(H.C.F) of 2880 and 2000 H.C.F of 2880 and 2000 is 80 $±\sqrt\frac{2880\div80}{2000\div80}=1+r$ $±\sqrt\frac{36}{25}=1+r$ $±\frac{6}{5}=1+r$ Step-6: Subtract both the sides with 1 and further simplify the left hand side $±\frac{6}{5}−1=r$ $\frac{±6-5}{5}=r$ Therefore,$ r=\frac{1}{5},\frac{−11}{5}$ Rate of Interest cannot be negative, hence, $r=\frac{1}{5}=0.2=$20%
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