An enterprise SH consumed 165.8 kWh during peak hours and 77 kWh during off-peak hours for a total cost of 22000f. During the same period, the enterprise MG consumed 55.3 kWh during peak hours and 22.1 kWh during off-peak hours for a total cost of 7000f. We need to determine the price of one kWh.

1. Problem Description

An enterprise SH consumed 165.8 kWh during peak hours and 77 kWh during off-peak hours for a total cost of 22000f. During the same period, the enterprise MG consumed 55.3 kWh during peak hours and 22.1 kWh during off-peak hours for a total cost of 7000f. We need to determine the price of one kWh.

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:

$165.8x + 77y = 22000$

$55.3x + 22.1y = 7000$

We can multiply the second equation by 77/22.1 = 3.484162896 to eliminate $y$:

$55.3 * (77/22.1)x + 22.1 * (77/22.1)y = 7000 * (77/22.1)$

$192.6334842x + 77y = 24389.14027$

Subtracting the first equation from the modified second equation, we get:

$(192.6334842 - 165.8)x + (77 - 77)y = 24389.14027 - 22000$

$26.8334842x = 2389.14027$

$x = \frac{2389.14027}{26.8334842} \approx 89.4043$

Now, substitute the value of $x$ back into the first equation:

$165.8(89.4043) + 77y = 22000$

$14822.93 + 77y = 22000$

$77y = 22000 - 14822.93$

$77y = 7177.07$

$y = \frac{7177.07}{77} \approx 93.2087$

The text asks to determine "le prix du kWh". Since there are two different prices, we have two values for it. If the question is intended to provide a single answer, there might be missing information, for instance, the problem might be aimed at finding an average price per kWh. Let's calculate the total kWh and total cost for both companies combined:

Total kWh = $165.8 + 77 + 55.3 + 22.1 = 320.2$ kWh

Total cost = $22000 + 7000 = 29000$

Average price per kWh = $\frac{29000}{320.2} \approx 90.57$

However, without further clarification, we can assume it asks for peak hour price and off-peak hour price.

3. Final Answer

The price per kWh during peak hours is approximately 89.40f.

The price per kWh during off-peak hours is approximately 93.21f.

Average price per kWh is approximately 90.57f.

If the question asks for a single price, then we can assume it is the average price 90.57f.