$344$ На покраску двух стен дома израсходовали $7$ , $26$ кг краски. Сколько килограммов краски было израсходовано на каждую стену, если площадь одной из них на $6$ м² $^{2}$ больше, чем площадь другой, а на каждый квадратный метр требуется $0$ , $22$ кг краски?

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344

На покраску двух стен дома израсходовали

7

26

кг краски. Сколько килограммов краски было израсходовано на каждую стену, если площадь одной из них на

6

м²

^{2}

больше, чем площадь другой, а на каждый квадратный метр требуется

0

22

кг краски?

Define Areas: Let's denote the area of the smaller wall as $A$ square meters. Then the area of the larger wall will be $A + 6$ square meters. Since $0.22 \, \text{kg}$ of paint is required per square meter, the total paint used for both walls is $7.26 \, \text{kg}$ .
Set Up Equation: We can set up the equation for the total paint used as follows: $\newline$ $0.22 \times A + 0.22 \times (A + 6) = 7.26$
Simplify Equation: Simplify the equation: $0.22A + 0.22A + 0.22 \times 6 = 7.26$
Combine Like Terms: Combine like terms: $0.44A + 1.32 = 7.26$
Isolate Term with A: Subtract $1.32$ from both sides to isolate the term with A: $\newline$ $0.44A = 7.26 - 1.32$
Calculate Right Side: Calculate the right side of the equation: $0.44A = 5.94$
Solve for A: Divide both sides by $0.44$ to solve for $A$ : $\newline$ $A = \frac{5.94}{0.44}$
Find Paint for Smaller Wall: Perform the division to find the area of the smaller wall: $A \approx 13.5 \, \text{m}^2$
Calculate Paint for Smaller Wall: Now we can find the amount of paint used for the smaller wall: $\newline$ Paint for smaller wall = $0.22 \times 13.5$
Find Area of Larger Wall: Calculate the paint used for the smaller wall: $\newline$ Paint for smaller wall $\approx 2.97$ kg
Calculate Area of Larger Wall: Next, we calculate the area of the larger wall, which is $A + 6$ : $\newline$ Area of larger wall = $13.5 + 6$
Find Paint for Larger Wall: Calculate the area of the larger wall: $\newline$ Area of larger wall = $19.5 \, \text{m}^2$
Calculate Paint for Larger Wall: Now we can find the amount of paint used for the larger wall: $\newline$ Paint for larger wall = $0.22 \times 19.5$
Check Total Paint Used: Calculate the paint used for the larger wall: Paint for larger wall $\approx 4.29$ kg
Check Total Paint Used: Calculate the paint used for the larger wall: $\newline$ Paint for larger wall $\approx 4.29$ kgFinally, we check if the total paint used for both walls adds up to the initial total of $7.26$ kg: $\newline$ Total paint used = Paint for smaller wall + Paint for larger wall $\newline$ Total paint used $\approx 2.97$ kg + $4.29$ kg
Check Total Paint Used: Calculate the paint used for the larger wall: $\newline$ Paint for larger wall $\approx 4.29$ kgFinally, we check if the total paint used for both walls adds up to the initial total of $7.26$ kg: $\newline$ Total paint used = Paint for smaller wall + Paint for larger wall $\newline$ Total paint used $\approx 2.97$ kg + $4.29$ kgCalculate the total paint used: $\newline$ Total paint used $\approx 7.26$ kg