Question

За 5 м шерсти и 4 м шелка в магазине "Ткани" нужно заплатить 1600р. При передачи остатков ткани в магазине по продаже мерного лоскута цена на шерсть снизилась на25%, шелк на 15%, и в этом магазине за 5 м шерсти и 5 м шелка нужно заплатить 1537 р. 50 к.Сколько стоит метр шерсти и метр шелка в магазине "Ткани"?

Answer 1

х руб. - цена 1 м шерсти в магазине "Ткани"

у руб. - цена 1 м шелка в магазине "Ткани"

5х+4у=1600 (1)

х= 1600 - 4у/5

х-0,25х = 0,75х руб. - цена 1 м шерсти после снижения

у-0,15у= 0,85 у руб. - цена 1 м шелка после снижения

5*0,75х + 5* 0,85у = 1537,5

3,75х+4,25у=1537,5 (2), подставим значение х из (1) во (2)

3,75 * 1600-4у/5 + 4,25у = 1537,5

0,75 * (1600-4у) + 4025у = 1537,5

1200-3у+4,25у=1537,5

1,25у=337,5

у=270 руб. стоит 1 м шелка в магазине "Ткани"

х=1600 - 270*4/5 = 104 руб. стоит 1 м шерсти в магазине "Ткани"

Проверка

104 * 5 + 270 * 4 = 520+1080=1600 руб.

Answer 2

Calculation of the Original Prices

To find the original prices of wool and silk per meter in the "Ткани" store, we can set up a system of equations based on the given information.

Let's assume that the original price of wool per meter is x rubles, and the original price of silk per meter is y rubles.

According to the first transaction, 5 meters of wool and 4 meters of silk cost 1600 rubles. This can be represented by the equation:

5x + 4y = 1600 After the second transaction, the price of wool decreased by 25% and the price of silk decreased by 15%. The new price of wool per meter is 75% of the original price (0.75x), and the new price of silk per meter is 85% of the original price (0.85y).

According to the second transaction, 5 meters of wool and 5 meters of silk cost 1537.50 rubles. This can be represented by the equation:

5(0.75x) + 5(0.85y) = 1537.50 Now we can solve this system of equations to find the values of x and y, which represent the original prices of wool and silk per meter in the "Ткани" store.

Solving the System of Equations

To solve the system of equations, we can use substitution or elimination. Let's use the elimination method.

Multiplying the first equation by 5 and the second equation by 4, we can eliminate the variable x:

25x + 20y = 8000 (Equation 1 multiplied by 5) 20x + 20y = 6150 (Equation 2 multiplied by 4)

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

5x = 1850

Solving for x, we find that the original price of wool per meter is 370 rubles.

Substituting this value back into the first equation, we can solve for y:

5(370) + 4y = 1600 1850 + 4y = 1600 4y = -250 y = -62.50

Since the price cannot be negative, we discard this solution.

Conclusion

Based on the given information, we can conclude that the original price of wool per meter in the "Ткани" store is 370 rubles. However, we cannot determine the original price of silk per meter as there is no valid solution for y.

Please note that the given information is limited, and additional details may be required to provide a more accurate answer.