The total average monthly cost of heat, power, and water for Sheridan Service for last year was $2010. If this year’s average is expected to increase by one-tenth over last year’s average, and heat is $22 more than three-quarters the cost of power, while water is $11 less than one-third the cost of power, how much should be budgeted on average for each month for each item?

Answer:Given,The total monthly budget of last year = $ 2010,∵ this year’s average is expected to increase by one-tenth over last year’s average,So, the total monthly budget of this year = 2010 + [tex]\frac{1}{10}[/tex] ( 2010)= 2010 + 201= $ 2211,Now, let the monthly budget for Power ( in dollars ) = P,∵ heat is $22 more than three-quarters the cost of power while water is $11 less than one-third the cost of power,So, budget for  heat = [tex]\frac{3}{4}P+22[/tex]Budget for  water = [tex]\frac{1}{3}P-11[/tex]Thus, total monthly budget = [tex]P+\frac{3}{4}P+22+\frac{1}{3}P-11[/tex][tex]=\frac{12P+9P+4P}{12}+11[/tex][tex]=\frac{25P}{12}+11[/tex][tex]\implies \frac{25P}{12}+11 = 2211[/tex][tex]\frac{25P}{12}=2200[/tex][tex]25P=26400[/tex][tex]\implies P = 1056[/tex]Hence, the budget, for power = $ 1056, For heat = [tex]\frac{3}{4}\times 1056+22=$ 814[/tex]For water = [tex]\frac{1}{3}\times 1056 - 11 = $ 341[/tex]