Chapter 5, Problem 14CT

(a)

To determine

To write: and sketch graph an inequality that represents the numbers of trophies and medals can buy.

Answer to Problem 14CT

The linear inequality is $12x+3y\le 60$ .

Explanation of Solution

Given information:

At most $60 to spend on trophies and medals to five as prizes for a contest.

Calculation:

Let $x$ be the number of trophies and $y$ be the number of medals. Then the inequalities that models the purchase with at most 60 dollars is

  $12x+3y\le 60$

Therefore, the linear inequality is $12x+3y\le 60$ .

Draw the graph $12x+3y\le 60$ as shown below. If only one item is purchase, either 20 trophies or 5 medals can be purchase as it clear from the graph.

  

(b)

To determine

To write: and sketch a graph of that represents the situation, and to find the number of given item can buy.

Answer to Problem 14CT

The linear inequality is $x+y\ge 6$ and $12x+3y\le 60$ .

Item can buy 2 trophies and 10 medals.

Explanation of Solution

Given information:

At most $60 to spend on trophies and medals to five as prizes for a contest.

Calculation:

If you want to purchase at least 6 items then the system of inequalities is

  $\begin{array}{l}12x+3y\le 60\\ x+y\ge 6\end{array}$

Therefore, the linear inequality is $x+y\ge 6$ and $12x+3y\le 60$ .

Draw the graph $x+y\ge 6$ and $12x+3y\le 60$ .as shown below. The ordered pair $\left(x,y\right)=\left(2,10\right)$ is in the solution set. It means item can buy 2 trophies and 10 medals.

  

Therefore, the graph of system of linear inequalities is drawn.