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

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 +
`(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 =
`(3)/(4)P+22`

Budget for water =
`(1)/(3)P-11`

Thus, total monthly budget =
`P+(3)/(4)P+22+(1)/(3)P-11`

`=(12P+9P+4P)/(12)+11`

`=(25P)/(12)+11`

`\implies (25P)/(12)+11 = 2211`

`(25P)/(12)=2200`

`25P=26400`

`\implies P = 1056`

Hence, the budget, for power = $ 1056,

For heat =
`(3)/(4)* 1056+22=$ 814`

For water =
`(1)/(3)* 1056 - 11 = $ 341`