Question

You budget $200 for wooden planks for outdoor furniture. Cedar costs $2.50 per foot and pine costs $1.75 per foot. Let x = the number of feet of cedar and let y = the number of feet of pine. What is an inequality that shows how much of each type of wood can be bought? Graph the inequality. What are three possible amounts of each type of wood that can be bought within your budget?

Answer 1

$2.50/ft * x + $1.75/ft *y ≤ $200

1. 80 feet of cedar
2. 10 feet of cedar, 100 feet of pine
3. 3 feet of cedar, 110 feet of pine

Answer 2

Givens

• The budget is $200
• Cedar costs $2.50 per foot
• Pine costs $1.75 per foot.

If
`x` represents the number of feet of cedar, and
`y` represents the number of feet of pine, the inequality that models this problem would be

`2.50x+1.75y\leq 200`

Where the restriction of 200 refers to the budget, which is the maximum amount possible.

If we graph this inequality, it would be like the image attached. The solution is the shaded area in the first quadrant of the system. Where a solution of this inequality would be (20,20), that is 20 feet of cedar and 20 feet of pine, this can be covered because is under $200, that is

`2.50(20)+1.75(20)=50+35=85`

Specifically, it costs $85.