Answer :
The cost charged by both contractors for a 1500 square foot cabin is $155,000.
To set up a system of linear equations for this problem, let's use the following variables:
- f: square feet of the cabin
- C1: cost charged by the first contractor
- C2: cost charged by the second contractor
According to the information provided, we can write the equations:
For the first contractor:
C1 = $5000 + $100f
For the second contractor:
C2 = $50000 + $70f
To obtain the number of square feet for which the two contractors charge the same amount, we need to solve the system of equations:
C1 = C2
Substituting the expressions for C1 and C2, we have:
$5000 + $100f = $50000 + $70f
To solve for f, we can simplify the equation:
$100f - $70f = $50000 - $5000
$30f = $45000
Dividing both sides by $30, we get:
f = $45000 / $30
Simplifying, we obtain:
f = 1500 square feet
Therefore, the two contractors will charge the same amount for a cabin with 1500 square feet.
To obtain the cost, we can substitute this value of f into either of the original equations:
C1 = $5000 + $100(1500)
= $5000 + $150000
= $155000
To know more about system of linear equations refer here:
https://brainly.com/question/20379472#
#SPJ11