QuestionFind the fence length where costs are equal: $20x + 210 = 27.50x$ . Simplify to find $x$ in feet.

Studdy Solution

STEP 1

Assumptions1. The first company charges $20 per foot of fence and a$ 210 installation fee. The second company charges $27.50 per foot of fence and has no installation fee3. The total cost for either company is the same

STEP 2

First, we need to set up an equation to represent the total cost for each company.For the first company, the total cost is the cost per foot times the length of the fence plus the installation fee.
For the second company, the total cost is just the cost per foot times the length of the fence.
So, we have $20x +210 =27.5x$ where x is the length of the fence.

STEP 3

Next, we need to solve the equation for x. Start by subtracting $20x$ from both sides to isolate the variable on one side of the equation.
$210 =7.5x$

STEP 4

Then, divide both sides by $7.$ to solve for x.
$x = \frac{210}{7.}$

STEP 5

Finally, calculate the value of x.
$x = \frac{210}{7.5} =28$ So, the fence would need to be28 feet long for the total cost to be the same for either company.

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