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: 67

Answer

Rate of interest is 20%.

Work Step by Step

Given: Amount (A) = 4320 Principal (P) = 3000 Time (t) = 2 We have to find the rate of interest i.e.$ r$. Step-1: Substitute the given values in the formula. $A=P(1+r)^t$ $4320=3000(1+r)^2$ Step-2: We now solve the equation for r. $4320=3000(1+r)^2$ Step-3: Divide both sides of the equation by 3000. $\frac{4320}{3000}=(1+r)^2$ Step-4: Use the square root property. $±\sqrt \frac{4320}{3000}=1+r$ Step-5: Simplify the left hand side by dividing the numerator and denominator by the Highest Common Factor(H.C.F) of 4320 and 3000 H.C.F of 4320 and 3000 is 120. $±\sqrt\frac{4320\div120}{3000\div120} =1+r$ $±\sqrt \frac{36}{25}=1+r$ $\frac{6}{5}=1+r$ 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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