Chapter 1.3, Problem 38E

a.

To determine

To use the given graph to determine after how many years there will be equal enrollment in Spanish and French classes.

Answer to Problem 38E

6

Explanation of Solution

Given:

  

The above graph shows two linear relations for students enrolled in French and Spanish with years passing by.

The above graph shows two linear relations for students enrolled in French and Spanish with years passing by.

Now, to find out that in which year the enrollment for will be equal, the intersection of both the graph has to be observed.

That point of intersection will be common for both the graphs.

Hence the point of intersection is:

No. of student enrolled in French language = 301

No. of student enrolled in Spanish language = 301

This date will occur after 6 years from when the data has been recorded.

Conclusion:

Hence, the required answer is 6 years.

b.

To determine

To justify estimation of subpart (a)

Explanation of Solution

Given:

  

Also,

  $355-9x=229+12x$

Here x has been considered as the years from the initial point.

Calculation:

Number of enrollment for French according to the table $=355-9x$

Number of enrollment for French according to the table $=299+12x$

Also, $355-9x=229+12x$ denotes the point where the number of enrollment for both the languages will be same and the solution will be point of intersection of the lines which is clearly visible in the graph.

Calculation:

Now, to find the solution:

  $\begin{array}{l}\Rightarrow 355-9x=229+12x\\ \Rightarrow 21x=126\\ \Rightarrow x=6\end{array}$

Hence, after solving the equation, it is justified that, the estimate made from the graph in part(a)

was correct.