integers word problems grade 7 | PPT - Free Printable

Problem Statement:

A certain freezing process requires that the room temperature be lowered from \(40^\circ \text{C}\) at a rate of \(5^\circ \text{C}\) every hour. What will be the room temperature 10 hours after the process begins?

---

Solution:

#### Step 1: Understand the given information
- Initial room temperature: \(40^\circ \text{C}\)
- Rate of cooling: \(5^\circ \text{C}\) per hour
- Time elapsed: 10 hours

#### Step 2: Determine the total change in temperature
The room temperature is decreasing at a constant rate of \(5^\circ \text{C}\) per hour. Over 10 hours, the total decrease in temperature can be calculated as:
\[
\text{Total decrease in temperature} = \text{Rate of cooling} \times \text{Time}
\]
\[
\text{Total decrease in temperature} = 5^\circ \text{C/hour} \times 10 \text{ hours} = 50^\circ \text{C}
\]

#### Step 3: Calculate the final temperature
The final temperature after 10 hours is obtained by subtracting the total decrease in temperature from the initial temperature:
\[
\text{Final temperature} = \text{Initial temperature} - \text{Total decrease in temperature}
\]
\[
\text{Final temperature} = 40^\circ \text{C} - 50^\circ \text{C} = -10^\circ \text{C}
\]

#### Step 4: Verify the result
- Starting at \(40^\circ \text{C}\), the temperature decreases by \(5^\circ \text{C}\) each hour.
- After 10 hours, the total decrease is \(50^\circ \text{C}\).
- Subtracting \(50^\circ \text{C}\) from \(40^\circ \text{C}\) gives \(-10^\circ \text{C}\).

This calculation is consistent and correct.

---

Final Answer:

\[
\boxed{-10^\circ \text{C}}
\]