Final answer:
To determine when the construction costs for both the football and baseball stadiums are the same, we set up equations for each stadium's costs and solve for the number of days. The costs equalize after approximately 4 days of construction.
Step-by-step explanation:
We need to find out when the construction costs for both the football and baseball stadiums are equal. The cost for constructing the football stadium is $2,580 plus $230 per day for labor. For the baseball stadium, the cost is $1,290 plus $552.50 per day for labor. Let's use the variable d to represent the number of days the construction takes.
For the football stadium, the cost can be represented as:
CostFootball = $2,580 + $230d
For the baseball stadium, the cost can be represented as:
CostBaseball = $1,290 + $552.50d
We set these equations equal to each other to find out when the costs are the same:
$2,580 + $230d = $1,290 + $552.50d
Solving for d, we get:
Subtract $1,290 from both sides:
$1,290 + $230d - $1,290 = $552.50d
Simplify:
$1,290 = $552.50d - $230d
Combine like terms:
$1,290 = $322.50d
Divide both sides by $322.50:
d = $1,290 / $322.50
Calculate the result:
d ≈ 4
So, after approximately 4 days, the construction costs for both stadiums will be the same.