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Question 1066242: You are an accountant for a construction business and are planning next year's budget. You have $200,000 to spend on salaries, equipment expenses, and other general expenses. Based on previous financial records of the business, you expect to spend five times as much on salaries as on equipment maintence, and you expect general expenses to be 10% of the amount spent on the other two combined. Write and solve a system of equations to find the amount you should budget for each category.
please kindly provide me the equations to use to solve this problem... thanks
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let g = amount for general expenses.
let e = amount for equipment expenses.
let s = amount for salaries.
total is 200,000.
g + e + s = 200,000
amount to be budgeted for salaries is 5 times amount to be budgeted for equipment expenses.
s = 5 * e
general expenses is expected to be 10% of the amount spent on the other two combined.
g = .10 * (s + e).
you have 3 equations to be solved simultaneously.,
they are:
s + e + g = 200,000
s = 5 * e
g = .10 * (s + e).
from g = .10 * (s + e), replace s with 5 * e from s = 5 * e to get:
g = .10 * (5 * e + e)
simplify to get g = .10 * 6 * e
simplify further to get g = .6 * e
from s + g + e = 200,000, replace s with 5 * e and replace g with .6 * e to get:
5 * e + .6 * e + e = 200,000
combine like terms to get 6.6 * e = 200,000
solve for e to get e = 200,000 / 6.6 = 30303.0303...
since s = 5 * e, you get s = 5 * 30303.0303 = 151515.1515...
since g = .10 * (s + e), you get g = .10 * (151515.1515... + 30303.0303...).
combine like terms to get g = .10 * 181818.1818...
solve for g to get g = 18181.81818...
s + g + e = 200,000 becomes 151515.1515... + 18181.81818... + 30303.0303... = 200,000.
simplify to get 200,000 = 200,000
solution looks good.
you should budget the following:
151515.1515... for salaries.
18181.81818... for general expenses.
30303.0303... for equipment expenses.
round those off to the nearest cent and you get:
151,515.15 for salaries.
18,181.82 for general expenses.
30,303.03 for equipment expenses.
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