Problem 44 - Algebra 1

Question

Match the real-life problem with an equation. Then solve the problem. A. \(x+15=7\) B. \(15-x=7\) C. \(15+7=x\) D. \(x+15=-7\) The temperature rose 15 degrees to \(7^{\circ} \mathrm{F}\). What was the original temperature?

Step-by-Step Solution

Answer

The original temperature was -8 degrees Fahrenheit.

Step 1: Match equation to situation

The temperature originally was \(x\) and it rose by 15 degrees to become 7 degrees. So, we add \(x\) and 15 to get 7. This corresponds to equation A, which is \(x+15=7\)

Step 2: Solve the equation

Our goal is to find the value of \(x\). We can subtract 15 from both sides of the equation. It now becomes \(x+15-15=7-15)\, so \, \(x=-8\).

Step 3: Interpret the result

The value of \(x\) which we found is the original temperature. So, the original temperature was -8 degrees Fahrenheit before it rose by 15 degrees.

Key Concepts

Solving Equations

When we're solving equations, our aim is to find the unknown value that makes the equation true. Equations are like puzzles where we already know the outcome, but we're missing one piece of information to complete it. Let's take this linear equation from our exercise:

• Start with the equation: \(x + 15 = 7\)
• We need to isolate \(x\) to find its value.
• To do this, perform the opposite operation to what's being done with \(x\). Here, it's adding 15, so we'll subtract 15 from both sides.

This gives us:\[ x + 15 - 15 = 7 - 15 \]After simplifying the above, we find:\[ x = -8 \]We've solved the equation and discovered that \(x\) is \(-8\). Solving equations is essential because it allows us to find unknowns in various situations, just like finding the starting temperature in a weather problem. By clearly following steps and handling operations carefully, solving equations becomes a straightforward process.

Real-life Applications

Applying math to real-life situations can make concepts easier to understand and more relatable. In our exercise, we're using temperature as an example, which is something we encounter regularly.

• Equations are used to solve problems such as calculating costs, predicting outcomes, and even in engineering.
• In a weather-related context, being able to find out the original temperature before a change helps us understand more about our environment.

Using equations allows us to translate real-world changes into math, equipping us better for daily decision-making and solving everyday problems. In this case, determining earlier temperatures can be crucial in planning for future weather changes. Understanding equations enhances critical thinking and problem-solving skills, applicable across various fields.

Temperature Changes

Temperature changes are common in our day-to-day lives. Understanding how to calculate them using equations allows us to gain insights into weather patterns and effects.When the problem states that the temperature rose by 15 degrees to reach 7°F, we use this information to set up an equation:

• The original temperature was the unknown, represented by \(x\).
• The temperature increased by 15 degrees, reaching a new temperature of 7°F.

Hence, the equation \(x + 15 = 7\) perfectly represents the situation.Solving this lets us backtrack to identify the temperature at an earlier time, providing insights such as forecasting and preparing for temperature fluctuations. By analyzing temperature changes, we can adjust expectations and plan accordingly, helping in various sectors—from agriculture to sports.