High School

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On vacation, Li's family will visit an amusement park. Riders must be at least 48 inches tall to ride the roller coaster. Li's little brother is 3 feet 8 inches tall. Which inequality can be used to find how many inches he must grow to be able to ride the roller coaster? (Given: [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 :

Let [tex]$h$[/tex] be the number of inches Li's little brother must grow. His current height is given as 42 inches, and he must reach at least 48 inches to ride the roller coaster. Therefore, his height after growing is expressed as

[tex]$$42 + h.$$[/tex]

Since he must be at least 48 inches tall, we set up the inequality

[tex]$$42 + h \ge 48.$$[/tex]

Rewriting the inequality in a form that matches the answer choices, we have

[tex]$$48 \le 42 + h,$$[/tex]

or equivalently

[tex]$$48 \le h + 42.$$[/tex]

Solving for [tex]$h$[/tex], we subtract 42 from both sides:

[tex]$$h \ge 48 - 42,$$[/tex]
[tex]$$h \ge 6.$$[/tex]

This calculation shows that he must grow at least 6 inches to be eligible. The correct inequality corresponding to this situation is

[tex]$$48 \le h + 42.$$[/tex]

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Rewritten by : Barada