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Hi - Work Problem










































four girls work together painting houses.For each house they paint they get $256.00 If the girls work for 4 monthes of the summer and thier expenses are $152.00 per month How many houses must they paint for each of them to have one thousand dollars at the end of the summer?

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Dec 22, 2011
Work vs Profit Calculation
by: Staff


Question:

four girls work together painting houses.For each house they paint they get $256.00 If the girls work for 4 monthes of the summer and thier expenses are $152.00 per month How many houses must they paint for each of them to have one thousand dollars at the end of the summer?



Answer:

Definition of VARIABLES:


M = number of months worked = 4

G = number of girls working = 4

H = number of houses painted = unknown

Gross revenue = H * ($256 in revenue per house)

Expenses = M * ($152 per month) = 4 * 152

Profit (desired) = G * ($1000 profit per girl) = 4 * 1000



Write the EQUATION:


Gross Revenue - Expenses = Profit

(H * 256) - (M * 152) = (G * 1000)


Substitute known values for variables

(H * 256) - (4 * 152) = (4 * 1000)


Solve for H

(H * 256) - (4 * 152) = (4 * 1000)

256H - 608 = 4000


Add 608 to each side of the equation. This will remove the 608 from the left side of the equation.

256H - 608 + 608 = 4000 + 608

256H + 0 = 4608

256H = 4608


Divide each side of the equation by 256. This will remove the 256 from the left side of the equation.

256H/256 = 4608/256

H*(256/256) = 4608/256

H*(1) = 4608/256

H = 4608/256

H = 18



The final answer: the girls must paint 18 houses for each of them to have one thousand dollars at the end of the summer



Check the answer by substituting 18 for H in the original equation

(H * 256) - (4 * 152) = (4 * 1000)

(18 * 256) - (4 * 152) = (4 * 1000)

(4608) - (608) = (4 * 1000)

4608 - 608 = 4000

4000 = 4000, OK → H = 18 is a VALID solution



Thanks for writing.


Staff
www.solving-math-problems.com


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