Answer
See below:
Work Step by Step
Put the value of B\[\left( 76,220 \right)\] in \[5.3x-y\ge 180\] and\[4.1x-y\le 140\] check for the inequality condition is satisfied.
Put B\[\left( 76,220 \right)\] in \[5.3x-y\ge 180\]
\[\begin{align}
& 5.3\times 76-220\ge 180 \\
& 402.8-220\ge 180 \\
& 182.8\ge 180
\end{align}\]
Solution exist because inequality condition is satisfied
Put B\[\left( 76,220 \right)\] in \[4.1x-y\le 140\]
\[\begin{align}
& 4.1\times 76-220\le 140 \\
& 311.6-220\le 140 \\
& 91.6\le 140
\end{align}\]
Solution exists because inequality condition is satisfied.
Hence, B\[\left( 76,220 \right)\] satisfy both the inequalities that describe healthy weight for this age group and solution also exist.
