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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 but no more than 145 pounds. Which inequality represents Carl's weight ([tex]x[/tex])?

a) [tex]130 \leq x \leq 145[/tex]
b) [tex]127 \leq x \leq 145[/tex]
c) [tex]127 \leq x \leq 148[/tex]
d) [tex]133 \leq x \leq 145[/tex]
e) [tex]133 \leq x \leq 148[/tex]

Answer :

Carl's weight must be less than or equal to 148 pounds which shows that option [tex]\[ \text{c) } 127 \leq x \leq 148 \][/tex] is correct.

Let's denote Carl's weight as [tex]\( x \).[/tex]

Corey weighs 127 pounds, Alex weighs at least 130 pounds but no more than 145 pounds. Therefore, we can represent Alex's weight as [tex]\( 130 \leq \text{Alex's weight} \leq 145 \).[/tex]

To find Carl's weight, we can subtract Corey and Alex's weights from the combined weight of all three friends:

[tex]\[ \text{Carl's weight} = \text{Total weight} - \text{Corey's weight} - \text{Alex's weight} \][/tex]

Given that the combined weight of Corey, Alex, and Carl is 405 pounds, and Corey weighs 127 pounds, we can express Carl's weight as:

[tex]\[ x = 405 - 127 - (\text{Alex's weight}) \][/tex]

Since Alex's weight is at least 130 pounds, we can use the lower bound of Alex's weight, which is 130:

[tex]\[ x = 405 - 127 - 130 \][/tex]

[tex]\[ x = 405 - 257 \][/tex]

[tex]\[ x = 148 \][/tex]

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