# 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?

### Comments for Hi - Work Problem

 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