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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?
Choose 1 answer:
(A)
500+4.50 M >= 5,000
(B)
4.50+500 M <= 5,000
(c)
500+4.50 M <= 5,000
(D)
500+4.50 M < 5,000

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? $\newline$ Choose $1$ answer: $\newline$ (A) $500+4.50 M \geq 5,000$ $\newline$ (B) $4.50+500 M \leq 5,000$ $\newline$ (C) $500+4.50 M \leq 5,000$ $\newline$ (D) 500+4.50 M<5,000

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Write a 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

Choose

1

answer:

\newline

(A)

500+4.50 M \geq 5,000

\newline

(B)

4.50+500 M \leq 5,000

\newline

(C)

500+4.50 M \leq 5,000

\newline

(D)

500+4.50 M<5,000

Identify Costs: Identify the fixed cost and the variable cost per thousand ad appearances. $\newline$ The fixed cost is a one-time charge of $\$500$ . The variable cost is $\$4.50$ for every one thousand times an advertisement is shown. The advertiser wants the ad to appear $M$ thousand times.
Write Total Cost: Write the total cost as an expression. $\newline$ The total cost is the sum of the fixed cost and the variable cost multiplied by the number of thousand ad appearances ( $M$ ). This gives us the expression $500 + 4.50M$ .
Set Budget Inequality: Set up the inequality based on the advertiser's budget constraint. $\newline$ The advertiser does not want to spend more than $\$5,000$ . Therefore, the total cost must be less than or equal to $\$5,000$ . This leads to the inequality $500 + 4.50M \leq 5,000$ .
Verify Matching Choice: Verify that the inequality matches one of the given choices. $\newline$ The inequality we have found, $500 + 4.50M \leq 5,000$ , matches choice (C).

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