Question

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 1

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 + $\frac{1}{10}$ ( 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 = $\frac{3}{4}P+22$

Budget for  water = $\frac{1}{3}P-11$

Thus, total monthly budget = $P+\frac{3}{4}P+22+\frac{1}{3}P-11$

$=\frac{12P+9P+4P}{12}+11$

$=\frac{25P}{12}+11$

$\implies \frac{25P}{12}+11 = 2211$

$\frac{25P}{12}=2200$

$25P=26400$

$\implies P = 1056$

Hence, the budget, for power = $ 1056,

For heat = $\frac{3}{4}\times 1056+22= 814$

For water = $\frac{1}{3}\times 1056 - 11 = 341$