Problem 442 - Prealgebra

Question

Distance Mayra lives 53 miles from her mother’s house and 71 miles from her mother- in-law’s house. How much farther is Mayra from her mother-in-law’s house than from her mother’s house?

Step-by-Step Solution

Answer

Mayra is 18 miles farther from her mother-in-law's house than from her mother's house.

Step 1 - Identify the distances

Determine the distances from Mayra's house to her mother's house and to her mother-in-law's house. These distances are given as 53 miles and 71 miles, respectively.

Step 2 - Set up the problem

The problem requires us to find how much farther Mayra is from her mother-in-law's house compared to her mother's house. This means we need to find the difference between these two distances.

Step 3 - Calculate the difference

Subtract the distance to her mother's house from the distance to her mother-in-law's house: Distance difference = 71 miles - 53 miles

Step 4 - Solve the equation

Perform the subtraction to find the difference: 71 miles - 53 miles = 18 miles

Key Concepts

distance calculation

To solve word problems that involve distance, it's crucial to understand how to calculate distances correctly. In our original exercise, Mayra’s distances to her mother's and mother-in-law's houses are given as 53 miles and 71 miles, respectively. These are straightforward distance values. Remember, distance is always a positive value reflecting how far one point is from another. Identifying these values correctly is the first essential step. We use the given numerical values directly in our calculations. Always ensure to check the units (miles in this case), as it can sometimes be kilometers or meters in other problems. The accuracy of your final answer depends heavily on these initial values. So, double-check these before moving on to further calculations.

subtraction

Subtraction is the mathematical process we use to find the difference between two numbers or quantities. When we're talking about distances, subtraction can help determine how much farther one point is compared to another. In our example, we need to find out how much farther Mayra's mother-in-law's house is compared to her mother’s house. This means subtracting the smaller distance (53 miles) from the larger distance (71 miles). Doing this step-by-step:

• Write down the two distances: 71 miles (mother-in-law's house) and 53 miles (mother's house).
• Perform the subtraction: \( 71 - 53 \).
• The result is 18 miles.

Subtraction in word problems is a straightforward but essential operation. Make sure to keep your equations organized and double-check your work to avoid mistakes.

problem-solving steps

Breaking down word problems into manageable steps is key to solving them accurately. Let’s revisit the original problem involving Mayra to understand this better. Following a structured approach:

• Step 1: Identify the Distances. Recognize the given distances: 53 miles and 71 miles.
• Step 2: Set Up the Problem. Understand what you need to find – the difference between these two distances.
• Step 3: Calculate the Difference. Use subtraction \( 71 - 53 \) to set up your calculation.
• Step 4: Solve the Equation. Perform the subtraction to get your answer: 18 miles.

Each of these steps is crucial for ensuring that you've understood the problem properly and are working towards the correct solution. Systematically work through each step and check your calculations to ensure accuracy. This methodical approach not only solves the problem at hand but also builds a solid foundation for tackling more complex problems in the future.