Answer:
b. (12, 485)
Step-by-step explanation:
We have been given the number of men receiving degrees (in thousands) is given by the equation [tex]y=3.6x+443[/tex], and for women, the equation is [tex]y=14.3x+317[/tex], where x is the number of years since 1970.
Let us find the coordinates of the point of intersection of both lines by equating our both equations as:
[tex]14.3x+317=3.6x+443[/tex]
[tex]14.3x-3.6x+317=3.6x-3.6x+443[/tex]
[tex]10.7x+317=443[/tex]
[tex]10.7x+317-317=443-317[/tex]
[tex]10.7x=126[/tex]
[tex]\frac{10.7x}{10.7}=\frac{126}{10.7}[/tex]
[tex]x=11.7757[/tex]
Upon substituting x=11.7757 in our equations we will get,
[tex]y=3.6x+443[/tex]
[tex]y=3.6*11.7757+443[/tex]
[tex]y=42.39252+443[/tex]
[tex]y=485.39252[/tex]
[tex]y=14.3x+317[/tex]
[tex]y=14.3*11.7757+317[/tex]
[tex]y=168.3925+317[/tex]
[tex]y=485.3925[/tex]
Upon rounding our answers to nearest whole number we will get,
[tex]y=485.3925\approx 485[/tex]
[tex]x=11.7757\approx 12[/tex]
Therefore, the point (12,485) will be the solution of our given equations and option b is the correct choice.
