Thinking Mathematically (6th Edition)

Published by Pearson

Chapter 6 - Algebra: Equations and Inequalities - 6.2 Linear Equations in One Variable and Proportions - Exercise Set 6.2 - Page 363: 107

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Work Step by Step

(a) Consider the equation as follows: $p+\frac{x}{2}=37$ Now, substitute the value of $x$as $\left( 2010-1970 \right)$and find the value of $p$. p+{( 2010-1970)}/{2}=37 p+{40}/{2}=37 p=37-20 =17% This shows that the mathematical model underestimates the percentage of American adults who smoked cigarettes in 2010. Now, subtract the above value of the percentage of American adults who smoked cigarettes in 2010from the given percentage of American adults who smoked cigarettes in 2010. We obtain: $19-17=2%$ Thus, the percentage is 17% and the mathematical model underestimates by 2%. (b) Consider the equation as follows: $p+\frac{x}{2}=37$ Now, substitute the value of $p$as $7$and find the value of $x$. \begin{align} & 7+\frac{x}{2}=37 \\ & \frac{x}{2}=37-7 \\ & x=60 \end{align} Here, the value of x represents the number of year after 1970. Now, the above conclusion gives the year as, \begin{align} & y=1970+x \\ & =1970+60 \\ & =2030 \end{align} Thus, this shows that only 7% Americans will smoke cigarettes in the year 2030.

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