Question

An accountant for a company is creating part of the fiscal budget for next year. She has $50,000 to allocate for salaries, insurance, and general expenses. Based on previous financial statements, she expects to spend eight times as much on salaries as on insurance. Also, general expenses historically cost 20% of the amount spent on salaries and insurance combined.

Write a system of equations for the amount allocated to each category. (Make certain to clearly define any variables you use.)

a) 8S + I + 0.2(8S + I) = 50000
b) S + 8I + 0.2(S + 8I) = 50000
c) 8S + I + 0.2(S + 8I) = 50000
d) S + I + 0.2(8S + I) = 50000

Answer 1

The system of equations for allocating the $50,000 budget to salaries, insurance, and general expenses are: 8I = S, 0.2(S + I) = G, and S + I + G = $50,000. This allows for calculating the amount to be allocated to each category.

Step-by-step explanation:

The accountant is trying to allocate a budget of $50,000 to three categories: salaries, insurance, and general expenses.

Let's define S as the money spent on salaries and I as the money spent on insurance. According to the given conditions, we have two equations to define the allocation:

1. The money spent on salaries is eight times the money spent on insurance:
   8I = S.
2. The general expenses are 20% of the combined salaries and insurance:
   0.2(S + I) = G, where G represents the general expenses.

The third equation, which sums up the allocation to a total of $50,000, can be written as:
S + I + G = $50,000.

The system of equations combining all the conditions would therefore be:

• 8I = S
• 0.2(S + I) = G
• S + I + G = 50,000

These equations can be used to find the values of S, I, and G that satisfy all conditions.