Question

If the temperature goes down \(33^{\circ} \mathrm{F}\), it will be \(-10^{\circ} \mathrm{F}\). What is the temperature now?

Short answer

The current temperature is \( 23^{\circ} \mathrm{F} \).

Step-by-step solution

Set Up the Equation

Let's denote the current temperature as \( T \). According to the problem, if the temperature (\( T \)) goes down by \( 33^{\circ} \mathrm{F} \), it will be \( -10^{\circ} \mathrm{F} \). This can be written as an equation: \( T - 33 = -10 \).

Solve for T

To find the current temperature \( T \), add \( 33 \) to both sides of the equation: \( T - 33 + 33 = -10 + 33 \). Simplifying this, we get: \( T = 23 \).

Verify the Solution

To ensure the answer is correct, subtract \( 33 \) from the current temperature \( 23^{\circ} \mathrm{F} \). \( 23 - 33 = -10 \), which matches the given condition. Thus, the solution is verified.

Key concepts

temperature change

Temperature change refers to the difference in temperature between two points in time. In this problem, we need to understand how a decrease in temperature impacts the current temperature. If the temperature drops by 33 degrees Fahrenheit, we need to calculate what the original temperature was. This involves using basic arithmetic to account for the change. Remember, understanding how temperature change works can help with similar problems where you need to find initial conditions before a change.

linear equations

Linear equations are mathematical expressions where variables are the first power (not squared or cubed, etc.). In this problem, the equation we formulated is linear:
\( T - 33 = -10 \). We use linear equations to set up relationships between variables and constants. To solve linear equations, we perform operations that isolate the variable (in this case, T). It’s important to understand that every step we take (like adding 33 to both sides) helps balance the equation and brings us closer to finding the unknown value.

problem-solving steps

Breaking down problems into manageable steps is crucial for solving them effectively. Here’s a structured way to tackle problems:

• Identify what you need to find.
• Set up an equation based on the problem statement.
• Perform operations to isolate the variable and solve for it.
• Verify your solution to ensure it satisfies the original problem.

For the current problem, this process involved defining a variable for the current temperature, formulating a linear equation, solving it by isolating the variable, and verifying the solution.

verification of solutions

Verifying solutions ensures they are correct and meet the problem's conditions. After solving for the temperature, we check our solution by substituting it back into the original context.
If the calculated temperature was 23°F, we check: \( 23 - 33 = -10 \). This step confirms that our equation setup and calculations were correct. Verification is important in all math problems to avoid mistakes. It provides confidence that our solution is accurate.