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Answer :
To find the inequality that represents Carl's weight, let's break down the problem step-by-step:
1. Understand the Problem Statements:
- The combined weight of Corey, Alex, and Carl is 405 pounds.
- Corey's weight is 127 pounds.
- Alex's weight is between 130 and 145 pounds.
2. Calculate Carl's Possible Weight:
- Let's use the formula for combined weight:
[tex]\[
\text{Corey's weight} + \text{Alex's weight} + \text{Carl's weight} = 405
\][/tex]
- Plug in the known values:
[tex]\[
127 + \text{Alex's weight} + \text{Carl's weight} = 405
\][/tex]
- To find Carl's weight, rearrange the equation in terms of Carl's weight:
[tex]\[
\text{Carl's weight} = 405 - 127 - \text{Alex's weight}
\][/tex]
3. Determine the Range for Carl's Weight:
- Substitute the minimum value of Alex's weight (130 pounds) to get the maximum possible weight for Carl:
[tex]\[
\text{Carl's weight max} = 405 - 127 - 130 = 148
\][/tex]
- Substitute the maximum value of Alex's weight (145 pounds) to get the minimum possible weight for Carl:
[tex]\[
\text{Carl's weight min} = 405 - 127 - 145 = 133
\][/tex]
4. Establish the Inequality:
- From these calculations, Carl's weight must be between 133 and 148 pounds. Thus, the inequality that represents Carl's weight [tex]\( x \)[/tex] is:
[tex]\[
133 \leq x \leq 148
\][/tex]
Therefore, the correct inequality for Carl's weight is [tex]\( 133 \leq x \leq 148 \)[/tex].
1. Understand the Problem Statements:
- The combined weight of Corey, Alex, and Carl is 405 pounds.
- Corey's weight is 127 pounds.
- Alex's weight is between 130 and 145 pounds.
2. Calculate Carl's Possible Weight:
- Let's use the formula for combined weight:
[tex]\[
\text{Corey's weight} + \text{Alex's weight} + \text{Carl's weight} = 405
\][/tex]
- Plug in the known values:
[tex]\[
127 + \text{Alex's weight} + \text{Carl's weight} = 405
\][/tex]
- To find Carl's weight, rearrange the equation in terms of Carl's weight:
[tex]\[
\text{Carl's weight} = 405 - 127 - \text{Alex's weight}
\][/tex]
3. Determine the Range for Carl's Weight:
- Substitute the minimum value of Alex's weight (130 pounds) to get the maximum possible weight for Carl:
[tex]\[
\text{Carl's weight max} = 405 - 127 - 130 = 148
\][/tex]
- Substitute the maximum value of Alex's weight (145 pounds) to get the minimum possible weight for Carl:
[tex]\[
\text{Carl's weight min} = 405 - 127 - 145 = 133
\][/tex]
4. Establish the Inequality:
- From these calculations, Carl's weight must be between 133 and 148 pounds. Thus, the inequality that represents Carl's weight [tex]\( x \)[/tex] is:
[tex]\[
133 \leq x \leq 148
\][/tex]
Therefore, the correct inequality for Carl's weight is [tex]\( 133 \leq x \leq 148 \)[/tex].
Thanks for taking the time to read Corey and his two friends Alex and Carl have a combined weight of 405 pounds Corey weighs 127 pounds Alex weighs at least 130 pounds. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
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