Two companies, SH and MG, consume electricity. Company SH consumes 165.8 kWh during peak hours and 77 kWh during off-peak hours for a total cost of 22000. Company MG consumes 55.3 kWh during peak hours and 22.1 kWh during off-peak hours for a total cost of 7000. The problem asks us to determine the price of kWh for peak and off-peak hours.

1. Problem Description

Two companies, SH and MG, consume electricity. Company SH consumes 165.8 kWh during peak hours and 77 kWh during off-peak hours for a total cost of

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0. Company MG consumes 55.3 kWh during peak hours and 22.1 kWh during off-peak hours for a total cost of

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0. The problem asks us to determine the price of kWh for peak and off-peak hours.

2. Solution Steps

Let $x$ be the price per kWh during peak hours and $y$ be the price per kWh during off-peak hours. We can set up a system of two linear equations based on the given information:

$165.8x + 77y = 22000$

$55.3x + 22.1y = 7000$

To solve this system, we can use the method of substitution or elimination. Let's use elimination. Multiply the second equation by $\frac{165.8}{55.3} = 3$ :

$3 * (55.3x + 22.1y) = 3 * 7000$

$165.9x + 66.3y = 21000$

This results in the following:

$165.8x + 77y = 22000$

$165.9x + 66.3y = 21000$

Subtracting the second equation from the first is not practical. So, instead, we proceed as follows.

Multiply the second equation by 77/22.1 which is approximately 3.

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4. $3.484 * (55.3x + 22.1y) = 3.484*7000$

$192.6652x + 77y = 24388$

Now we subtract the first equation from this:

$192.6652x + 77y - (165.8x + 77y) = 24388 - 22000$

$26.8652x = 2388$

$x = \frac{2388}{26.8652} \approx 88.89$

Now plug $x$ back into the first equation to solve for $y$:

$165.8(88.89) + 77y = 22000$

$14737.762 + 77y = 22000$

$77y = 22000 - 14737.762 = 7262.238$

$y = \frac{7262.238}{77} \approx 94.32$

3. Final Answer

The price per kWh during peak hours ($x$) is approximately 88.89 and the price per kWh during off-peak hours ($y$) is approximately 94.

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2. Peak hours: 88.89

Off-peak hours: 94.32