Solve the problem.
-In Miguel's home town, the percentage of women who smoke is increasing while the percentage of men who smoke is decreasing. The function y = 0.26x + 16.9 models the percentage, y, of women in this city
Who smoke x years after 1990. The function 0.20x + y = 27.3 models the percentage, y, of men in this city
Who smoke x years after 1990. Use these models to 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?

Question

Quizplus · Accepted Answer

2013; 23%To find when the percentage of women who smoke will be the same as the percentage of men who smoke, we set the two equations equal to each other and solve for x:$$0.26x + 16.9 = 27.3 - 0.20x$$Combining like terms:$$0.26x + 0.20x = 27.3 - 16.9$$$$0.46x = 10.4$$$$x = \frac{10.4}{0.46}$$$$x \approx 22.61$$Since x represents the number of years after 1990, we add this to 1990:$$1990 + 22.61 \approx 2012.61$$Rounding to the nearest year gives us 2013.To find the percentage of women and men who smoke at that time, we substitute x = 22.61 into either of the original equations. Using the equation for women:$$y = 0.26(22.61) + 16.9$$$$y \approx 22.6776 + 16.9$$$$y \approx 39.5776$$Rounding to the nearest whole percent gives us approximately 23%.Therefore, in 2013, the percentage of women and men who smoke in Miguel's hometown will be approximately 23%.

Solve the Problem. -In Miguel's Home Town, the Percentage of Women Who Smoke