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Question 1167611: The cost of running an paint shop businessis made up the following:
Office Rental= 40%
Labor = 35%
Materials = 20%
Miscellaneous = 5%
If the office rental increased by 24%, labor increase by 15%, cost of materials increased by 20% and the miscellaneouscosts are unchanged, find the percentage change in the cost of running the shop.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x equal the total.
Office Rental= 40% = .4 * x
Labor = 35% = .35 * x
Materials = 20% = .2 * x
Miscellaneous = 5% = .05 * x
total = x
If the office rental increased by 24%, labor increase by 15%, cost of materials increased by 20% and the miscellaneous costs are unchanged, find the percentage change in the cost of running the shop.
Office Rental= 40% = .4 * x * 1.24 = .496 * x
Labor = 35% = .35 * x * 1.15 = .4025
Materials = 20% = .2 * x * 1.2 = .24
Miscellaneous = 5% = .05 * x * 1 = .05
total = 1.1885 * x
overall increase is new value minus old value = 1.1885 * x - x = .1885 * x.
multiply that by 100 to get an increase of 18.85%.
percent = rate * 100
rate = percent / 100
details of office rental increase.
office rental = 40% * x = .4 * x
office rental is increased by 24%.
this gets you (.4 * x) + .24 * (.4 * x)
factor out the (.4 * x) to get (.4 * x) * (1 + .24)
simplify to get (.4 * x) * 1.24
solve to get 1.24 * .4 * x = .496 * x
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