Question

BAKERY Ben has $24 to spend on cookies and cupcakes. Write and graph an inequality that represents what Ben can buy.

Short answer

A graph of a given inequality is

The inequality is$2x+3y\le 24$.

Step-by-step solution

Step 1. Write given information in the form of inequality.

Let$x$be the number of cookies and$y$be the number of cupcakes. The cookies are $2 each, therefore, the cost of the cookies is$2x$.The cupcakes are $3 each, therefore, the cost of cupcakes is$3y$. As the Ben can spend no more than $24, the total cost must be less than or equal to $24. Therefore,

$2x+3y\le 24$

Step 2. Solve fory.

Solve for $y$in terms of $x$.

$\begin{array}{c}2x+3y-2x\le 24-2x\\ \frac{3y}{3}\le \frac{24-2x}{3}\\ y\le 8-\frac{2}{3}x\end{array}$

Step 3. Select a test point.

Let $(0,0)$be a test point. Substitute 0 for $x$and 0 for $y$into $y\le 8-\frac{2}{3}x$.

$\begin{array}{l}0\le 8-\frac{2}{3}\left(0\right)\\ 0\le 8\end{array}$

Therefore, the half plane containing the origin is the solution.

Step 4. Graph an inequality.

Graph an inequality,$2x+3y\le 24$and shade the half plane containing test point.