Question

A customer has $10 to spend at the concession stand. Hotdogs cost $2 each and drinks cost $2.50 each. Graph the inequality that illustrates this situation. Use the space below to explain what the answer means.

Answer 1

Please refer to the graph in the attached area.

Explanation:

Given:

Total money available with the customer is $10.

Cost of each hotdog is $2.

Cost of each drink is is $2.50.

To find:

The graph of inequality.

Solution:

Let number of hotdogs bought =
`x`

Total cost of hotdogs =
`2x`

Let number of drinks bought =
`y`

Total cost of drinks =
`2.5y`

Total cost =
`2x+2.5y`

And total money available is $10.

So, the total cost calculated above must be lesser than or equal to $10.

Hence, the inequality is:

`2x+2.5y<10`

Also there will be two conditions on variables
`x` and
`y`:

`x\ge0\\y\ge0`

To graph this, let us find the points on the equivalent equation:

`2x+2.5y = 10`

Finding two points on the equation.

First put x = 0
`\Rightarrow` y = 4

Then put y = 0,
`\Rightarrow` x = 5

So, two points are (0, 4) and (5, 0).

Now, plotting the line.

Having point (1,2) in the inequality:

2 + 5 < 10 (True) hence, the graph of inequality will contain the point (1,2)

Please refer to the graph of inequality in the attached graph.