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Sagot :
Certainly! Let's walk through the steps to solve the inequality for a person's healthy weight range, based on their height and Body Mass Index (BMI):
1. Understanding the Inequality:
The inequality given is:
[tex]\[ 18.5 \leq \frac{703 W}{74^2} \leq 24.9 \][/tex]
where:
- [tex]\( W \)[/tex] represents the weight in pounds.
- 74 inches is the person's height.
2. Isolate [tex]\( W \)[/tex]:
To find the weight range, we need to solve for [tex]\( W \)[/tex] in the inequality. We’ll start by isolating [tex]\( W \)[/tex] in the given inequality.
3. Expand and Isolate Step-by-Step:
The inequality can be split into two parts:
[tex]\[ 18.5 \leq \frac{703W}{5476} \quad \text{and} \quad \frac{703W}{5476} \leq 24.9 \][/tex]
4. Calculate Height Squared:
First, find the height squared:
[tex]\[ 74^2 = 5476 \][/tex]
5. First Part of the Inequality:
[tex]\[ 18.5 \leq \frac{703W}{5476} \][/tex]
- Multiply both sides by 5476 to isolate [tex]\( W \)[/tex]:
[tex]\[ 18.5 \times 5476 \leq 703W \][/tex]
- Calculate [tex]\( 18.5 \times 5476 \)[/tex]:
[tex]\[ 101306 \leq 703W \][/tex]
- Divide both sides by 703 to solve for [tex]\( W \)[/tex]:
[tex]\[ 144.10526315789474 \leq W \][/tex]
6. Second Part of the Inequality:
[tex]\[ \frac{703W}{5476} \leq 24.9 \][/tex]
- Multiply both sides by 5476 to isolate [tex]\( W \)[/tex]:
[tex]\[ 703W \leq 24.9 \times 5476 \][/tex]
- Calculate [tex]\( 24.9 \times 5476 \)[/tex]:
[tex]\[ 136256.4 \leq 703W \][/tex]
- Divide both sides by 703 to solve for [tex]\( W \)[/tex]:
[tex]\[ W \leq 193.9578947368421 \][/tex]
7. Combine the Results:
Combine the lower and upper bounds to specify the weight range:
[tex]\[ 144.10526315789474 \leq W \leq 193.9578947368421 \][/tex]
8. Conclusion:
The healthy weight range for a person who is 74 inches tall (6 feet 2 inches) is approximately:
[tex]\[ 144.11 \text{ pounds} \leq W \leq 193.96 \text{ pounds} \][/tex]
This interval represents the healthy weight range based on the given height and BMI boundaries.
1. Understanding the Inequality:
The inequality given is:
[tex]\[ 18.5 \leq \frac{703 W}{74^2} \leq 24.9 \][/tex]
where:
- [tex]\( W \)[/tex] represents the weight in pounds.
- 74 inches is the person's height.
2. Isolate [tex]\( W \)[/tex]:
To find the weight range, we need to solve for [tex]\( W \)[/tex] in the inequality. We’ll start by isolating [tex]\( W \)[/tex] in the given inequality.
3. Expand and Isolate Step-by-Step:
The inequality can be split into two parts:
[tex]\[ 18.5 \leq \frac{703W}{5476} \quad \text{and} \quad \frac{703W}{5476} \leq 24.9 \][/tex]
4. Calculate Height Squared:
First, find the height squared:
[tex]\[ 74^2 = 5476 \][/tex]
5. First Part of the Inequality:
[tex]\[ 18.5 \leq \frac{703W}{5476} \][/tex]
- Multiply both sides by 5476 to isolate [tex]\( W \)[/tex]:
[tex]\[ 18.5 \times 5476 \leq 703W \][/tex]
- Calculate [tex]\( 18.5 \times 5476 \)[/tex]:
[tex]\[ 101306 \leq 703W \][/tex]
- Divide both sides by 703 to solve for [tex]\( W \)[/tex]:
[tex]\[ 144.10526315789474 \leq W \][/tex]
6. Second Part of the Inequality:
[tex]\[ \frac{703W}{5476} \leq 24.9 \][/tex]
- Multiply both sides by 5476 to isolate [tex]\( W \)[/tex]:
[tex]\[ 703W \leq 24.9 \times 5476 \][/tex]
- Calculate [tex]\( 24.9 \times 5476 \)[/tex]:
[tex]\[ 136256.4 \leq 703W \][/tex]
- Divide both sides by 703 to solve for [tex]\( W \)[/tex]:
[tex]\[ W \leq 193.9578947368421 \][/tex]
7. Combine the Results:
Combine the lower and upper bounds to specify the weight range:
[tex]\[ 144.10526315789474 \leq W \leq 193.9578947368421 \][/tex]
8. Conclusion:
The healthy weight range for a person who is 74 inches tall (6 feet 2 inches) is approximately:
[tex]\[ 144.11 \text{ pounds} \leq W \leq 193.96 \text{ pounds} \][/tex]
This interval represents the healthy weight range based on the given height and BMI boundaries.
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