Chapter 5.6, Problem 18E

To determine

To find: whether the person received $A$ on the test.

Answer to Problem 18E

  $x=20\text{ and }y=18$ is the solution of the given inequality.

Explanation of Solution

Given:

The inequality:

  $3x+2y\ge 93$ .

Concept used:

Inequality tell us relative size of the two values.

Like a value can be greater or lesser or equal.

  $2<3,4>2\text{ and }2=2.$

In a graph inequality is shown in the area of shaded region.

This sign $\le \text{ or}\ge$ is also used normally when there is unknown variable exist.

  $x\le 5,y\ge 2$ .

Calculation:

Check whether answering $20$ multiple choice questions and $18$ matching questions correctly gives an $A$ in the test as shown below.

That is $x=20\text{ and }y=18.$

Substituting the $x=20\text{ and }y=18.$ in the inequality $3x+2y\ge 93.$ .

  $\begin{array}{l}3x+2y\ge 93.\\ 3\left(20\right)+2\left(18\right)\ge 93.\\ 96\ge 93.\end{array}$

Which is true.

therefore, answering $20$ multiple choice questions and $18$ matching questions correctly gives an $A$ in the test.

Hence, $x=20\text{ and }y=18.$ is the solution of the given in equality.