Answer:
a. x = 12
b. 12 years after 1970, the number of men graduating equals the number of women graduating.
c.
Explanation:
We have the system
[tex]\begin{gathered} y=3.7x+441 \\ y=14.4x+314 \end{gathered}[/tex]
and we solve it by substituting the value of y from the first equation into the second equation:
[tex]14.4x+314=3.7x+441[/tex]
subtracting 314 from both sides gives
[tex]14.4x=3.7x+127[/tex]
subtracting 3.7 from both sides gives
[tex]10.7x=127[/tex]
Finally, dividing both sides by 127 gives
[tex]x=\frac{127}{10.7}[/tex][tex]\boxed{x=11.869\ldots}[/tex]
which rounded to the nearest whole number is
[tex]\boxed{x=12}[/tex]
The solution tells us that 12 years after 1970, the number of men graduating equals the number of women graduating.
The graph of the equations is given below:
By looking at the slope we see that more women graduate than men and after 12 years, the number of graduating women is greater than men.
