# Chapter 6 - Algebra: Equations and Inequalities - 6.3 Applications of Linear Equations - Exercise Set 6.3: 7

The number is 320.

#### Work Step by Step

step 1 Let x represent the unknown number in the problem. step 2 "$70\%$ of a number" = $\displaystyle \frac{70}{100}\cdot x=0.7x$ " is $224$" is written as " = $224$" step 3 The equation is $0.7x=224$ step 4 $0.7x=224\qquad/\div 0.7$ $x=\displaystyle \frac{224}{0.7}=\frac{2240}{7}=320$ The number is $320$. step 5 Check the solution in the original wording of the problem. $7$0% of $340,$ ($\displaystyle \frac{70}{100}\cdot 320=224),$ is 224. OK.

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