Problem 136 - Intermediate Algebra

Question

In the following exercises, solve. Football On first down, the Steelers had the ball on their 30 -yard line. They gained 9 yards on the firstdown play, lost 14 yards on the second-down play, and lost 2 yards on the third-down play. What was the yard line at the end of the third-down play?

Step-by-Step Solution

Answer

The yard line at the end of the third-down play is 23 yards.

Step 1 - Initial Position

The Steelers started on their own 30-yard line. Represent this starting position as: Initial Position = 30 yards

Step 2 - First Down

On the first down play, they gained 9 yards. Add this gain to the initial position: New Position = 30 + 9 New Position = 39 yards

Step 3 - Second Down

On the second down play, they lost 14 yards. Subtract this loss from the current position: New Position = 39 - 14 New Position = 25 yards

Step 4 - Third Down

On the third down play, they lost 2 yards. Subtract this loss from the current position: New Position = 25 - 2 New Position = 23 yards

Key Concepts

headline of the respective core concept

Understanding integer operations is essential when dealing with algebra word problems. In this problem, we encounter both addition and subtraction, which are basic integer operations. Remember, when you add a positive number, you move to the right on a number line. When you subtract a positive number or add a negative one, you move to the left.
In the context of our football scenario:

• First, we add 9 to the initial yard line (a positive move).
• Second, we subtract 14 (a backward move).
• Finally, we subtract 2 more (another backward move).

Practicing these operations helps you maintain accuracy. Always check your calculations step-by-step to avoid errors. Integer operations form the foundation for more complex algebraic concepts.

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Following a step-by-step solution approach makes solving word problems systematic and manageable. Here, we break down the football problem into clear, manageable steps.

• Step 1: Identify the starting yard line (30 yards).
• Step 2: Calculate the new position after gaining 9 yards (30 + 9 = 39 yards).
• Step 3: Account for the loss of 14 yards (39 - 14 = 25 yards).
• Step 4: Subtract the final loss of 2 yards (25 - 2 = 23 yards).

By organizing the steps, we ensure clearer understanding and fewer mistakes. This method applies not only to algebra problems but across various mathematical disciplines. It’s all about clarity and confidence in each step.

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Applied mathematics uses real-world scenarios to teach mathematical concepts. This problem is an example of how algebra applies to everyday situations like sports. The key here is to translate words into mathematical operations.

• The initial position is given in terms of yards.
• Changes in yards are described by gains and losses.
• These changes follow integer operations — addition and subtraction.

By converting the football yard line movements into mathematical steps, students see the practical side of algebra. Applied mathematics makes abstract concepts tangible, reinforcing their importance and usefulness outside the classroom.