Question

you can spend at most $20 on tomatoes and red peppers for a soup. tomatoes cost $2.50 per pound and red peppers cost $4 per pound. write and graph an inequality that represents the amounts of tomatoes and red peppers you can buy.

Answer 1

`\boxed{\boxed{2.50x+4y\leq 20}}`

Solution-

The total money that you have or maximum amount that you can spend = $20

Let's assume,

x = Number of tomatoes bought

y = Number of red peppers bought

Price of tomatoes per pound = $2.50

Price of red peppers per pound = $4

Hence,

Total cost of tomatoes = $2.5x

Total cost of red peppers = $4y

As you can spend at most (any amount less than or equal to) $20, so

`2.5x+4y\leq 20`

Taking a point as origin (0, 0) and then putting it in the equation,

`\Rightarrow 2.5(0)+4(0)\leq 20\\\\\Rightarrow 0\leq 20`

As this satisfies, so the shaded region will be towards that point i.e origin

From the graph, the two solutions that are on the boundary line are (8, 0), (5, 0)