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A particular company charges advertisers a one time cost of $\$500$ , in addition to $\$4.50$ for every one thousand times an advertisement is shown on the company's webpage. An advertiser wants its ad to appear $M$ thousand times on the webpage, but does not want to spend more than $\$5,000$ . Which of the following inequalities best describes the situation? $\newline$ Choices: $\newline$ (A) $500+4.50M\geq5,000$ $\newline$ (B) $4.50+500M>5,000$ $\newline$ (C) $500+4.50M\leq5,000$ $\newline$ (D) $500+4.50M<5,000$

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Linear Inequality Word Problems

Full solution

Q. A particular company charges advertisers a one time cost of

\$500

, in addition to

\$4.50

for every one thousand times an advertisement is shown on the company's webpage. An advertiser wants its ad to appear

M

thousand times on the webpage, but does not want to spend more than

\$5,000

. Which of the following inequalities best describes the situation?

\newline

Choices:

\newline

(A)

500+4.50M\geq5,000

\newline

(B)

4.50+500M>5,000

\newline

(C)

500+4.50M\leq5,000

\newline

(D)

500+4.50M<5,000

Calculate Total Cost: Fixed cost is \$\(500\), and the variable cost is \$\(4\).\(50\) per thousand times the ad is shown. So, the total cost for \(M\) thousand times is \(\$500 + \$4.50 \times M\).
Set Budget Limit Inequality: The advertiser's budget cannot exceed \(\$5,000\). So, the inequality should represent the total cost being less than or equal to \(\$5,000\).
Formulate Inequality: Set up the inequality: \(\$500 + \$4.50 \times M \leq \$5,000\).
Choose Correct Inequality: Now, we need to choose the correct inequality from the given choices that matches our inequality. The correct choice is \([500+4.50M\leq5,000]\).

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