Question

The water level in a tank is lowered by 6 inches, then raised by \(8\frac{1}{2}\) inches, and then lowered by 4 inches. If the water level was x inches before the changes in level, which of the following represents the water level, in inches, after the changes?

• A. $x - 1 \dfrac{1}{2}$
• B. $x + 1 \dfrac{1}{2}$
• C. $x - 6 \dfrac{1}{2}$
• D. $x + 6 \dfrac{1}{2}$
• E. $x - 18 \dfrac{1}{2}$

Hint:

When dealing with word problems involving sequential changes, write down the expression as you read it. Combine all the positive changes and all the negative changes separately before finding the net change to reduce errors. In this case: Net Change = \(+8.5 - 6 - 4 = 8.5 - 10 = -1.5\).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This problem requires translating a series of described changes into a mathematical expression. The initial level is \(x\), and we need to apply the changes sequentially. "Lowered" implies subtraction, and "raised" implies addition.
Step 2: Detailed Explanation:
Let's track the water level step-by-step.
1. The initial water level is \(x\) inches.
2. The level is lowered by 6 inches. The new level is \(x - 6\).
3. Then, the level is raised by \(8\frac{1}{2}\) inches. The new level is \((x - 6) + 8\frac{1}{2}\).
4. Finally, the level is lowered by 4 inches. The final level is \((x - 6) + 8\frac{1}{2} - 4\).
Step 3: Simplifying the Expression:
Now, we simplify the expression by combining the constant terms.
\[ \text{Final Level} = x - 6 + 8\frac{1}{2} - 4 \] We can group the constants:
\[ (-6 - 4) + 8\frac{1}{2} = -10 + 8\frac{1}{2} \] To subtract, we can think of it as \(8.5 - 10\):
\[ -10 + 8.5 = -1.5 \] So, the total change is \(-1.5\) inches, which is the same as \(-1\frac{1}{2}\) inches.
The final water level is:
\[ x - 1\frac{1}{2} \] Step 4: Final Answer:
The expression representing the final water level is \(x - 1\frac{1}{2}\).