Answer:
the 4th company should receive 4x = 4($9,375) = $37,500 for their part in the project.
Explanation:
We can solve this problem by working backwards from the total amount of money spent on the project and using the proportions of the work completed by each company to determine their respective earnings.
Let's denote the amount of work completed by the 4th company as x. Then, according to the problem statement:
The 3rd company will complete 4x amount of work.
The 1st company will complete 3 times the amount of work completed by the 3rd company, so it will complete 3(4x) = 12x amount of work.
The 2nd company will complete twice the amount of work completed by the 1st company, so it will complete 2(12x) = 24x amount of work.
Therefore, the total amount of work completed by all four companies is:
x + 4x + 12x + 24x = 41x
We know that the total cost of the project is $4,100,000, so we can set up the following equation based on the proportion of the work completed by each company to the total amount of work:
Total cost of project = Cost for 4th company + Cost for 3rd company + Cost for 1st company + Cost for 2nd company
Simplifying this equation using the proportions of work completed by each company, we get:
$4,100,000 = x + 4(4x) + 3(4x)(3) + 2(4x)(12)
Simplifying and solving for x, we get:
x = $9,375
Therefore, the 4th company should receive 4x = 4($9,375) = $37,500 for their part in the project.