Question

A person can spend at most $12 on Corn oil and cereal.A bottle of corn oil cost $3 and a box of cereal cost $2.Identify the inequality and graph the equation for a situation where X is the number of bottles of corn oil and Y is the number of boxes of cereal.

Answer 1

Since x is the number of bottles of corn oil, and each bottle costs $3, so the cost for these bottles is 3x.

If y is the number of boxes of cereal, and each box costs $2, so the cost for these boxes is 2y.

Adding these two costs, the total cost is 3x + 2y.

This cost needs to be smaller than or equal to $12, so we can write the following inequality:

`3x+2y\le12`

In order to graph this inequality, let's find two ordered pairs that are solutions to the corresponding equation.

To do so, let's choose values for x and then calculate the corresponding values of y:

`\begin{gathered} 3x+2y=12 \\ x=2\colon \\ 6+2y=12\to2y=6\to y=3 \\ x=4\colon \\ 12+2y=12\to2y=0\to y=0 \end{gathered}`

The equation line will be the line that passes through the points (2, 3) and (4, 0).

Since the symbol of the inequality is "smaller than or equal to", the solution is the region below the line, and the line itself is part of the solution.

Graphing this, we have: