91影视

Let

$$\begin{gathered} x=numberofproteinbars \\ y=numberofbottlesofjuice \end{gathered}$$

Philip's has to consume at least $1000$calories where each protein jar has $140$calories and a bottle of juice has $125$calories. So,

$140x+125y鈮�1000$

$\$1.80$for protein jar and $\$1.25$for a bottle of protein must not be more than $\$12$. So,

$1.80x+1.25y鈮�12$

The number of protein bars is equal or greater than zero. So,

$x鈮�0$

The number of bottles is equal or greater than zero.

$y鈮�0$

The obtained system of inequalities

role="math" localid="1644507063721" $\left\{\begin{array}{l}140x+125y鈮�1000\\ 1.80x+1.25y鈮�12\\ x鈮�0\\ y鈮�0\end{array}\right.$

The graph for the obtained system of inequalities is:

To determine if he can buy $3$protein bars and $5$bottles of juice, we look at the graph to see if the point $\left(3,5\right)$is in the solution region (dark blue).

Yes, it is in the solution region. So Philip can buy $3$protein bars and $5$bottles of juice.

o determine if he can buy $5$protein bars and $3$bottles of juice, we look at the graph to see if the point $\left(5,3\right)$is in the solution region (dark blue).

No, it is not in the solution region. So Philip cannot buy $5$protein bars and $3$bottles of juices.