Final answer:
The firm employs 12 senior workers and 60 junior workers. The number of each type of worker is found by solving a system of two equations derived from the firm's total weekly wage bill and the ratio of junior to senior workers.
Step-by-step explanation:
The question involves solving a system of equations to determine the number of junior and senior workers employed at a firm. We can set up two equations based on the information given: Let S be the number of senior workers and J be the number of junior workers. The first equation is J = 5S, which comes from the statement that the firm has five times as many junior workers as senior workers. The second equation is 620S + 460J = 43,800, which represents the total weekly wage bill.
To find the solution, substitute the first equation into the second one, resulting in 620S + 460(5S) = 43,800. Solving for S gives us the number of senior workers, and multiplying that by five gives us the number of junior workers. After calculating these values, we find that there are 12 senior workers and 60 junior workers employed at the firm.
The total weekly wage bill plays a crucial role in setting up the equations and finding the solution. This type of problem is an excellent example of practical application of mathematics in business settings.