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In the town of Milton Lake, the percentage of women who smoke is increasing while the percentage of men who smoke is decreasing. Let x represent the number of years since 1990 and y represent the percentage of women in Milton Lake who smoke. The graph of y against x includes the data points (0, 15.9) and ( 13, 19.67). Let x represent the number of years since 1990 and y represent the percentage of men in Milton Lake who smoke. The graph of y against x includes the data points (0, 29.7) and ( 15, 26.85). Determine when the percentage of women who smoke will be the same as the percentage of men who smoke. Round to the nearest year. What percentage of women and what percentage of men (to the nearest whole percent) will smoke at that time? [Hint: first find the slope-intercept equation of the line that models the percentage, y, of women who smoke x years after 1990 and the slope-intercept equation of the line that models the percentage, y, of men who smoke x years after 1990]

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Kalahira
The slope-intercept equation for the percent of women y that smoke and x years since 1990 is y = (29/100)x + 15.9.

The slope-intercept equation for the percent of men y that smoke and x years since 1990 is y = (-19/100)x + 29.7. Slope was found by assigning (x1,y1) and (x2,y2) values to the given coordinates. Y-intercept is simply the y-value where x = 0. (The first coordinate given in each set) After 28.75 years the percents of men and women smokers will be the same. This is found by making each equation equal to the other. The percent of men and women smokers will be about 24.2%. Found by substituting 28.75 into either equation for x.