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Answer :
To solve the problem of determining Nelia's weight at the end of the year, follow these steps:
1. Initial Weight: Nelia starts the year weighing 112 lbs.
2. First Quarter Change: She gains [tex]\(4 \frac{2}{3}\)[/tex] lbs. To work with this fraction, convert it into a decimal:
- [tex]\(4 \frac{2}{3} = 4 + \frac{2}{3} \approx 4.67\)[/tex]
3. Third Quarter Change: Later in the year, she loses [tex]\(2 \frac{1}{5}\)[/tex] lbs. Let's convert this fraction to a decimal too:
- [tex]\(2 \frac{1}{5} = 2 + \frac{1}{5} \approx 2.20\)[/tex]
4. Last Quarter Change: By the end of the year, Nelia gains [tex]\(3 \frac{3}{4}\)[/tex] lbs. Again, convert this mixed number to a decimal:
- [tex]\(3 \frac{3}{4} = 3 + \frac{3}{4} \approx 3.75\)[/tex]
5. Calculate Final Weight: Add up the weight gained and subtract the weight lost from her initial weight:
- Start with the initial weight: 112 lbs
- Add the gain from the first quarter: [tex]\(112 + 4.67 = 116.67\)[/tex]
- Subtract the loss from the third quarter: [tex]\(116.67 - 2.20 = 114.47\)[/tex]
- Finally, add the gain from the last quarter: [tex]\(114.47 + 3.75 = 118.22\)[/tex]
So, Nelia's weight at the end of the year is approximately [tex]\(118.22\)[/tex] lbs.
Among the given options, the closest to this result is:
- c) [tex]\(118 \frac{13}{60} \text{ lbs}\)[/tex]
This is the correct answer.
1. Initial Weight: Nelia starts the year weighing 112 lbs.
2. First Quarter Change: She gains [tex]\(4 \frac{2}{3}\)[/tex] lbs. To work with this fraction, convert it into a decimal:
- [tex]\(4 \frac{2}{3} = 4 + \frac{2}{3} \approx 4.67\)[/tex]
3. Third Quarter Change: Later in the year, she loses [tex]\(2 \frac{1}{5}\)[/tex] lbs. Let's convert this fraction to a decimal too:
- [tex]\(2 \frac{1}{5} = 2 + \frac{1}{5} \approx 2.20\)[/tex]
4. Last Quarter Change: By the end of the year, Nelia gains [tex]\(3 \frac{3}{4}\)[/tex] lbs. Again, convert this mixed number to a decimal:
- [tex]\(3 \frac{3}{4} = 3 + \frac{3}{4} \approx 3.75\)[/tex]
5. Calculate Final Weight: Add up the weight gained and subtract the weight lost from her initial weight:
- Start with the initial weight: 112 lbs
- Add the gain from the first quarter: [tex]\(112 + 4.67 = 116.67\)[/tex]
- Subtract the loss from the third quarter: [tex]\(116.67 - 2.20 = 114.47\)[/tex]
- Finally, add the gain from the last quarter: [tex]\(114.47 + 3.75 = 118.22\)[/tex]
So, Nelia's weight at the end of the year is approximately [tex]\(118.22\)[/tex] lbs.
Among the given options, the closest to this result is:
- c) [tex]\(118 \frac{13}{60} \text{ lbs}\)[/tex]
This is the correct answer.
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