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**Writing an Inequality**

On vacation, Li's family will be visiting an amusement park. Riders must be at least 48 inches tall to go on the roller coaster. Li's little brother is 3 feet 6 inches tall. Which inequality can be used to find how many inches he must grow to be able to ride the roller coaster?

(Note: [tex]12 \text{ in.} = 1 \text{ ft}[/tex])

A. [tex]48 \geq h - 42[/tex]

B. [tex]48 \leq h - 42[/tex]

C. [tex]48 \geq h + 42[/tex]

D. [tex]48 \leq h + 42[/tex]

Answer :

First, convert Li's little brother's height from feet and inches to inches. Since 1 foot equals 12 inches, his height is calculated as follows:
[tex]$$
3\text{ ft }6\text{ in } = 3 \times 12 + 6 = 36 + 6 = 42 \text{ inches}.
$$[/tex]

Next, let [tex]$h$[/tex] be the number of inches he must grow. Since the minimum height required to ride the roller coaster is 48 inches, his future height must satisfy:
[tex]$$
42 + h \geq 48.
$$[/tex]

To express the inequality in a form resembling the choices, rewrite the inequality:
[tex]$$
42 + h \geq 48 \quad \Longleftrightarrow \quad 48 \leq 42 + h.
$$[/tex]

Thus, the inequality that can be used to find the number of inches he must grow is:
[tex]$$
48 \leq h + 42.
$$[/tex]

This corresponds to the fourth option in the list.

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Rewritten by : Barada