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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: 12 in. = 1 ft)

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 :

Sure! Let's solve the problem step by step.

1. Understand the problem requirements:
- Riders need to be at least 48 inches tall to get on the roller coaster.

2. Determine Li's little brother's current height in inches:
- He is 3 feet 6 inches tall.
- Since 1 foot equals 12 inches, we first convert the feet into inches:
[tex]\(3 \text{ feet} = 3 \times 12 = 36 \text{ inches}\)[/tex].
- Add the remaining 6 inches:
[tex]\(36 \text{ inches} + 6 \text{ inches} = 42 \text{ inches}\)[/tex].

3. Calculate how many more inches he needs to grow:
- Li's little brother is currently 42 inches tall and needs to be at least 48 inches tall.
- Subtract his current height from the minimum required height:
[tex]\(48 \text{ inches} - 42 \text{ inches} = 6 \text{ inches}\)[/tex].
- So, he needs to grow 6 more inches.

4. Set up the inequality:
- To determine how many inches he needs to grow, we use the inequality:
[tex]\(48 \geq 42 + g\)[/tex].
- Here, [tex]\(g\)[/tex] represents the number of inches he needs to grow to be able to ride the roller coaster.

The correct inequality to find how many inches Li's little brother must grow is [tex]\(48 \geq 42 + g\)[/tex].

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