Question

the pattern of higher rates of current alcohol use, binge alcohol use, and heavy alcohol use among full - time college students than among others aged 18 to 22 has remained consistent since 2002. using data from 2002 to 2008, the equations representing the percents of young adults aged 18 to 22 who used alcohol are shown below, where x represents the number of years after 2000.
enrolled in college ( y=-0.279x + 19.879 )
not enrolled ( y=-0.057x + 13.413 )
solve this system to determine when the percent for those enrolled in college will equal that for those not enrolled. what will the percent be?
in the year (square) (round up to the nearest year.)
the percent of young adults aged 18 to 22 using alcohol will be (square%) (round to the nearest whole number as needed.)

Explanation:

Step1: Set equations equal

$-0.279x + 19.879 = -0.057x + 13.413$

Step2: Isolate x terms

$-0.279x + 0.057x = 13.413 - 19.879$

Step3: Calculate coefficients/constants

$-0.222x = -6.466$

Step4: Solve for x

$x = \frac{-6.466}{-0.222} \approx 29.126$

Step5: Find calendar year

$2000 + 29.126 \approx 2029.126$

Step6: Calculate alcohol percent

Substitute $x \approx 29.126$ into $y = -0.057x + 13.413$:
$y = -0.057(29.126) + 13.413 \approx -1.660 + 13.413 = 11.753$

Answer:

In the year 2030, the percent for those enrolled in college will equal that for those not enrolled.
The percent of young adults aged 18 to 22 using alcohol will be 12%.