The average annual number of cigarettes smoked by an adult in some country continues to decline....

Question:

The average annual number of cigarettes smoked by an adult in some country continues to decline. For the years 1997-2006, the equation y = -49.2x + 1756.7 approximates this data. Here x is the number of years after 1997 and y is the average annual number of cigarettes smoked.

If this trend continues, find the year in which the average annual number of cigarettes smoked is zero.

Solving Word Problems with Linear Equations:

In mathematics, when a word problem involves a linear equation, we can solve the word problem by using the information presented in the problem and that equation to find the unknown quantity in the problem. We do this by plugging in given values in the equation, and then solving for the remaining variable as we would in any linear equation.

Answer and Explanation:

We are given that the equation {eq}y=-49.2x+1756.7 {/eq} approximates the average annual number of cigarettes smoked by an adult in a certain country x years after 1997. We want to know how long it will take for the average annual number of cigarettes smoked to reach 0 if this trend continues. Since y is the average annual number of cigarettes smoked, and we want to know when this will reach 0, we want to find x when y = 0. Thus, we plug 0 in for y in the equation, and solve for x.

  • {eq}y=-49.2x+1756.7 {/eq}

Plug in 0 for y.

  • {eq}0=-49.2x+1756.7 {/eq}

Subtract 1756.7 from both sides of the equation.

  • {eq}-1756.7=-49.2x {/eq}

Divide both sides of the equation by -49.2.

  • {eq}35.7\approx x {/eq}

We get that x ≈ 35.7 when y = 0. Therefore, the average annual number of cigarettes smoked will reach 0 approximately 35.7 years after 1997, or during the year that is 35 years past 1997. Thus, we add 35 to 1997 to determine this year.

  • {eq}1997+35=2032 {/eq}

We get that, if this trend continues, then the average number of cigarettes smoked by an adult in this country will reach 0 in the year 2032.


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Understanding the Steps in Solving an Equation

from NC EOC Assessment - Math I: Test Prep & Practice

Chapter 5 / Lesson 2
892

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