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Mary plans to buy $5$ tickets to go to an orchestra concert with her friends. She expects to spend at least $\$90$ on the tickets. $\newline$ Let $x$ represent how much Mary expects each ticket to cost. Which inequality describes the problem? $\newline$ Choices: $\newline$ (A) $5x \geq 90$ $\newline$ (B) 5x < 90 $\newline$ Solve the inequality. Then, complete the sentence to describe the solution. $\newline$ Mary expects each ticket to cost at least $\$\_$ .

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One-step inequalities: word problems

Full solution

Q. Mary plans to buy

5

tickets to go to an orchestra concert with her friends. She expects to spend at least

\$90

on the tickets.

\newline

Let

x

represent how much Mary expects each ticket to cost. Which inequality describes the problem?

\newline

Choices:

\newline

(A)

5x \geq 90

\newline

(B)

5x < 90

\newline

Solve the inequality. Then, complete the sentence to describe the solution.

\newline

Mary expects each ticket to cost at least

\$\_

.

Understand Problem & Inequality: Step $1$ : Understand the problem and set up the inequality. $\newline$ Mary plans to buy $5$ tickets and expects to spend at least $\$90$ . This means the total cost for $5$ tickets should be no less than $\$90$ . We represent the cost of each ticket by $x$ . $\newline$ The inequality that describes this situation is $5x \geq 90$ .
Identify Correct Choice: Step $2$ : Identify the correct inequality choice. $\newline$ From the choices given: $\newline$ (A) $5x \geq 90$ $\newline$ (B) 5x < 90 $\newline$ Choice (A) correctly represents the situation where Mary expects to spend at least $\$90$ on $5$ tickets.
Solve the Inequality: Step $3$ : Solve the inequality. $\newline$ To find the minimum cost per ticket, solve the inequality $5x \geq 90$ . $\newline$ Divide both sides by $5$ : $\newline$ $x \geq \frac{90}{5}$ $\newline$ $x \geq 18$

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