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Solve a one-step real-world problem involving multiplication with rational numbers.

Lake Profondo has a depth of 84 feet. Lake Segundo is 5/6 as deep. What is the elevation at the bottom of Lake Segundo? (Remember, the elevation is below sea level. Account for this in your answer.)
Answer: -70 ft.

3 answers

To find the depth of Lake Segundo, we need to multiply the depth of Lake Profondo by the fraction that represents Lake Segundo's depth relative to Lake Profondo.

Here's the calculation:

  1. Lake Profondo's depth: 84 feet
  2. Lake Segundo is \( \frac{5}{6} \) as deep as Lake Profondo.

To find the depth of Lake Segundo, we multiply:

\[ \text{Depth of Lake Segundo} = \text{Depth of Lake Profondo} \times \frac{5}{6} = 84 \times \frac{5}{6} \]

Calculating this step by step:

\[ = \frac{84 \times 5}{6} \]

First, calculate \( 84 \times 5 \):

\[ 84 \times 5 = 420 \]

Now divide by 6:

\[ \frac{420}{6} = 70 \]

Therefore, the depth of Lake Segundo is 70 feet. Since this depth is below sea level, we express it as a negative number for elevation:

\[ \text{Elevation at the bottom of Lake Segundo} = -70 , \text{ft} \]

Thus, the answer is indeed:

-70 ft.

Account for this in your answer.)

To account for the negative elevation when referencing depths below sea level, let's summarize the problem and the steps clearly, maintaining a focus on the context provided.

Problem:

Lake Profondo has a depth of 84 feet. Lake Segundo is \( \frac{5}{6} \) as deep as Lake Profondo. We need to find the elevation at the bottom of Lake Segundo, remembering that the elevation is below sea level.

Calculation Steps:

  1. Determine the depth of Lake Segundo: \[ \text{Depth of Lake Segundo} = \text{Depth of Lake Profondo} \times \frac{5}{6} \]

  2. Substituting the values: \[ = 84 \times \frac{5}{6} \]

  3. Calculating the product:

    • First, multiply: \[ 84 \times 5 = 420 \]
    • Then, divide by 6: \[ \frac{420}{6} = 70 \]

  4. Conclusion on depth: Therefore, the depth of Lake Segundo is 70 feet.

  5. Expressing the elevation: Since this is below sea level, we need to express this depth as a negative elevation: \[ \text{Elevation at the bottom of Lake Segundo} = -70 , \text{ft} \]

Final Answer:

Thus, the elevation at the bottom of Lake Segundo, accounting for its depth below sea level, is:

\[ \text{-70 feet} \]