Answer
a) $6$ years
b) See the explanation
Work Step by Step
a) The number of students enrolled is taken on the $y$ axis and the year taken is taken on the $x$ axis. As per the graph, the point where the two lines of the subjects meet is when the number of students enrolled was equal ($300$ students). The year corresponding to $300$ in $x$ axis is $6$.
b) As per the table, the present enrollments for Spanish is $355$. Also, it is expected to decrease by $9$ students every year. So after $x$ years., the number of enrollments will be $355 - 9x$.
Similarly, for French, the current enrollments is $229$. The enrollments are expected to increase by $12$ students every year. Hence, after $x$ years, the total number of enrollments so far will be $229+ 12x$.
In part a), we were supposed to find out the year, $x$, when the total enrollments for both subjects become equal. Hence $355 - 9x$ becomes equal to $229+12x$. We solve the equation: $$355 - 9x = 229 + 12x.$$ Add $9x$ to both sides: $$355 = 229 + 21 x.$$ Subtract $229$ from both sides: $$126 = 21 x.$$ Divide both sides by $21$: $$6 = x.$$ Therefore, $6$ years from now is when the total enrollments for Spanish and French become equal. This is same as the answer in part a).
