Chapter 8, Problem 49CR

To determine

Write and solve the inequality to show the maximum number of CDs Jose can buy

Answer to Problem 49CR

Jose can buy a maximum number of CDs is $6$

Explanation of Solution

Given:

Jose is buying books and CDs. He can spent at most $150. He spends $30 on books. If each CD costs $20

Concept Used:

• If there is the strict inequality symbol $<\text{ or}>$ , then use a parenthesis $\left(\right)$ on the interval
• If there is the inequality symbol $\le \text{ or}\ge$ , then use a bracket $\left[\right]$ on the interval

Calculation:

In order to find that the equality. Let x be the number of CDs Jose can buy. the product of the cost of per CDs and the number of CDs plus the cost of books must be less than or equal to 150.Now to simplify further use the basic algebraic orations to solve for x as below:

  $\begin{array}{l}20x+30\le 150\\ 20x+30-30\le 150-30\\ 20x\le 120\\ \frac{20x}{20}\le \frac{120}{20}\\ x\le 6\end{array}$

Thus, Jose can buy a maximum number of CDs is $6$