Chapter SH, Problem 3.7EP

a.

To determine

To write and graph: of a system of inequalities to represent the situation.

Answer to Problem 3.7EP

  $\begin{array}{l}x+y=2000\\ x\ge 875\\ y\ge 800\end{array}$ .

Explanation of Solution

Given:

The total score on a college entrance exam for the math and verbal section is 2000. the college requires a math score at least 875 and verbal score of at least 800. $\$35$ .

Calculation:

Consider the score in math is x and in verbal sections is y .

As the total score for the college entrance exam is 2000 therefore,

  $x+y=2000$

The college requires a math score of at least 875 and a verbal score of at least 800 hence

  $\begin{array}{l}x\ge 875\\ y\ge 800\end{array}$

Hence, the complete situation is,

  $\begin{array}{l}x+y=2000\\ x\ge 875\\ y\ge 800\end{array}$

Use maple to plot the graph of the above situation as shown below:

  

b.

To determine

To give: two examples of acceptable math and verbal scores for the entrance to the college.

Answer to Problem 3.7EP

  $\$147.5$ .

Explanation of Solution

Given:

The total score on a college entrance exam for the math and verbal section is 2000. the college requires a math score at least 875 and verbal score of at least 800.

Calculation:

From the above graph, there is two acceptable scores $\left(875,1125\right)$ and $\left(1200,800\right)$ .

Hence, the first example of acceptable math and verbal scores for the entrance to the college will be:

The second example of acceptable math and verbal scores for the entrance to the college will be: