A dog kennel owner needs to build a dog run (rectangular area) adjacent to a kennel cage (so that it is in the shape of a rectangle, but only three sides need to be built- one long side is already there). The short side walls of the run are to be cinder block (costs $0.50 per square foot) and the outer walls are to be chain link fence ($2.75 per square foot). Local regulations require the walls to be at least seven feet high and the are to measure no fewer than 120 square feet.

Any help would be greatly appericiated! I can't seem to find an equation with only one variable.

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To calculate the cost of building the dog run, we need to determine the dimensions of the run that meet the requirements and then calculate the cost based on the type of material used.

Let's assume the width of the dog run is "w" feet and the length (adjacent to the kennel cage) is "l" feet. As per the requirements, the dimensions must result in an area of at least 120 square feet, and the walls must be at least 7 feet high.

We can start by setting up an equation for the area of the dog run:
Area = Length × Width

According to the problem, the length is already given and we assume a width of "w" feet. So the equation becomes:
Area = l × w

From this equation, we can solve for w:
w = Area / l

Now, we can calculate the cost of the dog run based on the two types of material used: cinder block and chain link fence.

The cost of the cinder block walls is $0.50 per square foot, while the cost of the chain link fence is $2.75 per square foot.

First, we need to calculate the area of the cinder block walls:
Cinder block area = 2 × (Height × Width)

Since the height and width of the cinder block walls are the same as the width of the dog run, we can substitute "Width" into the equation:
Cinder block area = 2 × (7 × w)

Next, we calculate the area of the chain link fence:
Chain link area = 2 × (Height × Width) + Length × Height

Since the height is 7 feet and the dimensions are the same as the dog run, we can substitute the values:
Chain link area = 2 × (7 × w) + l × 7

Finally, we can determine the cost of each type of material by multiplying the area by the cost per square foot:
Cinder block cost = Cinder block area × $0.50
Chain link cost = Chain link area × $2.75

Adding these two costs together will give us the total cost of building the dog run.

In summary:
1. Calculate the width of the dog run using the equation: w = Area / l
2. Calculate the area of the cinder block walls: Cinder block area = 2 × (7 × w)
3. Calculate the area of the chain link fence: Chain link area = 2 × (7 × w) + l × 7
4. Calculate the cost of the cinder block walls: Cinder block cost = Cinder block area × $0.50
5. Calculate the cost of the chain link fence: Chain link cost = Chain link area × $2.75
6. Add the cinder block cost and chain link cost to get the total cost of building the dog run.