Absolute Value Word Problem - YouTube - Free Printable

You're on the right track! Let's go through the problem step by step and solve it clearly.

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Problem:

The average January temperature in a northern Canadian city is 1 degree Fahrenheit. The actual January temperature may be about 5 degrees warmer or colder than the average. We are to find the minimum and maximum possible temperatures.

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Step 1: Set up the equation

Let $ t $ represent the actual January temperature.

Since the temperature can vary by up to 5 degrees from the average (1°F), we use an absolute value equation:

$$
|t - 1| = 5
$$

This means the difference between the actual temperature $ t $ and the average (1°F) is 5 degrees.

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Step 2: Solve the absolute value equation

We break this into two cases:

#### Case 1: $ t - 1 = 5 $

Add 1 to both sides:
$$
t = 5 + 1 = 6
$$

#### Case 2: $ t - 1 = -5 $

Add 1 to both sides:
$$
t = -5 + 1 = -4
$$

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Step 3: Interpret the results

- Maximum temperature: 6°F
- Minimum temperature: -4°F

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✔ Answer:

The minimum temperature is -4°F, and the maximum temperature is 6°F.

So, the actual January temperature in the city could range from -4°F to 6°F.

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✔ Final Answer:

- Minimum temperature: $ \boxed{-4^\circ\text{F}} $
- Maximum temperature: $ \boxed{6^\circ\text{F}} $

Let me know if you'd like a graph or number line representation!