## Algebra: A Combined Approach (4th Edition)

Published by Pearson

# Chapter 11 - Section 11.1 - Solving Quadratic Equations by Completing the Square - Practice: 10

#### Answer

Interest rate is 5%

#### Work Step by Step

Given: Amount (A) = 1764 Principal (P) = 1600 Time (t) = 2 We have to find the rate of interest i.e. $r$ Step-1: Substitute the given values in the formula $A=P(1+r)^t$ $1764=1600(1+r)^2$ Step-2: We now solve the equation for $r$ $1764=1600(1+r)^2$ Step-3: Divide both sides of the equation by $1600$ $\frac{1764}{1600}=(1+r)^2$ Step-4: Use the square root property $±\sqrt (\frac{1764}{1600})=1+r$ $±\frac{42}{40}=1+r$ Step-5: Simplify the left hand side by dividing the numerator and denominator by the Highest Common Factor(H.C.F) of 42 and 40 H.C.F of 42 and 40 is 2 $±\frac{42\div2}{40\div2}=1+r$ $±\frac{21}{20}=1+r$ 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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