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On a particular weight loss television show, a person weighed 271 lbs, lost 9 lbs, gained 4 lbs, lost 12 lbs, and lost 24 lbs. Describe this weight fluctuation with a sum of integers and find the final weight of the contestant.



Select the correct choice below and fill in the answer box to complete your choice. (Simplify your answer.)


A$271+{ }^{-} 9+{ }^{-} 4+{ }^{-} 12+{ }^{-} 24=$ □ lbs
B$271+{ }^{-} 9+{ }^{-} 4+12+{ }^{-} 24=$ □ lbs
C$271+9+4+12+24=$ □ lbs
D$271+{ }^{-} 9+4+{ }^{-} 12+{ }^{-} 24=$ □ lbs
E$271+9+{ }^{-} 4+12+24=$ □ lbs

F. $271+{ }^{-} 9+{ }^{-} 4+12+24=$ □ lbs

Verified Answer :

  • Represent each weight loss as a negative integer and each gain as a positive integer.
  • The expression for the total fluctuation is \(271 + (-9) + 4 + (-12) + (-24)\), which corresponds to option D.
  • Perform the arithmetic: \(271 - 9 + 4 - 12 - 24 = 230\).
  • The final weight of the contestant is \(\boxed{230} \text{ lbs}\).

Explanation

  1. Analyzing and Modeling Weight Fluctuations

The problem asks us to determine the final weight of a contestant on a weight loss show, starting from an initial weight of 271 lbs. Throughout the show, the contestant experiences several weight changes, which can be modeled using addition and subtraction of integers. We represent a 'weight loss' as a negative value (subtraction) and a 'weight gain' as a positive value (addition). Starting weight is \(271\) lbs. The changes are:

  • Loss of 9 lbs corresponds to \(-9\).
  • Gain of 4 lbs corresponds to \(+4\).
  • Loss of 12 lbs corresponds to \(-12\).
  • Loss of 24 lbs corresponds to \(-24\).

Combining these, the expression for the total weight fluctuation is \(271 + (-9) + 4 + (-12) + (-24)\). Comparing this to the given choices, we identify that Option D is the correct mathematical representation.

  1. Calculating the Final Weight

To find the final weight, we evaluate the expression \(271 + (-9) + 4 + (-12) + (-24)\) step-by-step:

  1. Start with the initial weight: \(271\).
  2. Subtract 9 lbs: \(271 - 9 = 262\).
  3. Add 4 lbs: \(262 + 4 = 266\).
  4. Subtract 12 lbs: \(266 - 12 = 254\).
  5. Subtract 24 lbs: \(254 - 24 = 230\).

Therefore, the final weight of the contestant is 230 lbs. The correct option is D, represented as \(271 + (-9) + 4 + (-12) + (-24) = 230\).

Examples

Understanding how to track weight fluctuations using positive and negative numbers is a basic but essential skill in personal health management. Just as we did here, you can track your own progress by maintaining a simple log: record your initial weight, then add (+) or subtract (-) every gain or loss you experience over time. This helps you visualize your trends, celebrate your successes, and stay motivated toward your health goals!

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