Chapter 5.6, Problem 17E

To determine

To find: whether the carpenter buy twelve $2\times 8$ boards and fourteen $4\times 4$ boards.

Answer to Problem 17E

  $x=12\text{ and }y=14$ is the solution of the given inequality.

Explanation of Solution

Given:

Carpenter has at most $\$250$ .

  $2\times 8$ boards and fourteen $4\times 4$ board.

  $8x+12y\le 250.$

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:

The objective is to find whether the carpenter can buy twelve $2\times 8$ boards and fourteen $4\times 4$ board from the given in equality.

Consider the inequality as:

  $8x+12y\le 250.$

Here, $x$ is the number of $2\times 8$ boards and the number of $4\times 4$ boards.

Check whether the carpenter can buy twelve $2\times 8$ boards and fourteen $4\times 4$ boards or not.

That is $x=12\text{ and }y=14.$

Substituting the $x=12\text{ and }y=14.$ in the inequality $8x+12y$ .

  $\begin{array}{l}8x+12y\le 250.\\ 8\left(12\right)+12\left(14\right)\le 250.\\ 240\le 250.\end{array}$

Which is true.

therefore, the carpenter can buy twelve $2\times 8$ boards and fourteen $4\times 4$ board from the given in equality.

Hence, $x=12\text{ and }y=14$ is the solution of the given in equality.