Difficulty: Medium
Correct Answer: 210.085
Explanation:
Introduction:
This question checks your comfort with decimal arithmetic and simple equation balancing. You are given a numerical expression and an equation involving a missing value x. The goal is to evaluate the left side and then solve for x on the right side.
Given Data / Assumptions:
Concept / Approach:
First, compute the value of the left hand side by adding and subtracting the decimals. Then equate this result to 123.6 + x. Solving for x is done by subtracting 123.6 from the total. Working carefully with decimal places ensures accuracy.
Step-by-Step Solution:
Step 1: Add the first two numbers: 138.009 + 341.981.Step 2: 138.009 + 341.981 = 479.990 (since 0.009 + 0.981 = 0.990 and 138 + 341 = 479).Step 3: Subtract 146.305 from this sum: 479.990 − 146.305.Step 4: Perform the subtraction: 479.990 − 146.305 = 333.685.Step 5: Now the equation becomes 333.685 = 123.6 + x.Step 6: To find x, subtract 123.6 from 333.685.Step 7: 333.685 − 123.600 = 210.085.Step 8: Therefore x = 210.085.
Verification / Alternative check:
Substitute x = 210.085 back into the right side: 123.6 + 210.085 = 333.685, which matches the left side value. This confirms that the solution is correct and consistent.
Why Other Options Are Wrong:
199.57, 295.05, and 120.085 do not satisfy the equation when substituted for x, because 123.6 plus any of these values does not equal 333.685. The option “None of these” is incorrect because a valid correct value, 210.085, is present among the options.
Common Pitfalls:
Errors often arise from misalignment of decimal points during addition and subtraction. Another common mistake is forgetting to subtract 123.6 from the total to isolate x. Writing the intermediate steps clearly and keeping decimal places lined up helps avoid such errors.
Final Answer:
The value of x that makes the equation true is 210.085.
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