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?
Show Hint
- $x - 1 \dfrac{1}{2}$
- $x + 1 \dfrac{1}{2}$
- $x - 6 \dfrac{1}{2}$
- $x + 6 \dfrac{1}{2}$
- $x - 18 \dfrac{1}{2}$
The Correct Option is A
Solution and Explanation
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 \(x - 1\frac{1}{2}\).
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