High School

A scuba diver is at an elevation of -25 feet. She starts moving at a rate of -10 feet per minute. Which inequality represents how long it will take the diver to reach an elevation deeper than -220 feet?

A. [tex]-10x - 25 \leq -220[/tex]

B. [tex]-10x - 25 \geq -220[/tex]

C. [tex]-10x - 25 < -220[/tex]

D. [tex]-10x - 25 > -220[/tex]

Answer :

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

1. Understanding the Problem:
- The scuba diver starts at an elevation of -25 feet.
- She is descending at a rate of -10 feet per minute.
- We want to find out how long it takes for her to reach an elevation deeper than -220 feet.

2. Setting Up the Inequality:
- We need to express the diver's depth at any time [tex]\( x \)[/tex] in minutes. Her depth can be represented by the equation: [tex]\( \text{Current depth} = -10x - 25 \)[/tex].
- We want this depth to be deeper than -220 feet, so we set up the inequality:
[tex]\[
-10x - 25 < -220
\][/tex]

3. Solving the Inequality:
- First, isolate the term with [tex]\( x \)[/tex]:
[tex]\[
-10x < -220 + 25
\][/tex]
Simplifies to:
[tex]\[
-10x < -195
\][/tex]

- Next, divide both sides by -10. Remember, when you divide or multiply an inequality by a negative number, the inequality sign flips:
[tex]\[
x > \frac{-195}{-10}
\][/tex]

4. Calculate the Solution:
- Calculate the right side of the inequality:
[tex]\[
x > 19.5
\][/tex]

5. Conclusion:
- It will take the diver more than 19.5 minutes to reach an elevation deeper than -220 feet.

The correct inequality is [tex]\( -10x - 25 < -220 \)[/tex], which is option (C).

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