
To write: An inequality to express the given inequality and also to obtain the graph of the same.

Answer to Problem 14QC
The inequality can be expressed as,
The minimum number of sweatshirt to be sold for the given condition is 100 and the number of T-shirts is 167.
Explanation of Solution
Given Information:
The price for a T-shirt is $15 and for a sweatshirt is $25. The total money made out of selling a set of T-shirts and sweatshirts should be at least $2500 in order to cover the expenses.
Formula used:
The following approach is used to obtain an inequality showing the number of T-shirts and sweatshirts to be sold
(1) Assuming two variables corresponding to the number of T-shirts and sweatshirts
(2) Using the cost of single entity, the total selling cost for T-shirts and sweatshirts can be obtained.
(3) The minimum money to be obtained is given and the inequality can be therefore formed as the total amount obtained out of selling is to be greater than or equal to the minimum amount.
Once the inequality is obtained, the graph can be sketched using suitable tool.
Calculation:
Let the number of T-shirts sold be x and number of sweatshirts sold be y. Here, the cost of single T-shirt is $15 and the cost of one sweatshirt is $25. Therefore the total amount obtained by selling the given number of shirts is expressed as,
The minimum amount to be earned is $2500. Therefore the inequality can be expressed as,
Therefore the number of T-shirts and sweatshirts to be sold is such that the above inequality is satisfied.
Now, the graph of the given inequality is as follows.
From the graph, it is clear that, the minimum number of sweatshirt to be sold for the given condition is 100 and the number of T-shirts is 167.
Chapter 3 Solutions
Glencoe Algebra 2 Student Edition C2014
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