Question

На 5 га участка фермер посадил виноград, а на 3 га этого же участка - клубнику. На 3 га второго участка он посадил виноград, а на 5 га этого же участка - клубнику. С первого участка он собрал 55,5 ц, а со второго - 54,1 ц винограда и клубники. Сколько центнеров винограда собрал фермер с 1 га? Сколько центнеров клубники?

Answer 1

Пусть х центнеров винограда собрал фермер с 1 га участка, а у  центнеров клубники собрал фермер с 1 га.

Составим систему уравнений:
 5х+3у=55,5
3х+5у=54,1    
(обозначить систему скобкой { )

Метод сложения:  
5х+3у=55,5  (умножим на 3)
3x+5у=54,1  (умножим на 5)  

15х+9у=166,5
15x+25y=270,5  

 _15x+9у=166,5 
   15x+25у=270,5
     15х-15х+9у-25у=166,5-270,5
   -16у=-104
     16у=104
у=6,5 центнеров клубники собрали с 1 га. 

5х+3у=55,5
5х+3*6,5=55,5
5х+19,5=55,5
5х=55,5-19,5
5х=36
х=36:5
х=7,2 центнера винограда собрали с 1 га.

Ответ: с 1 га участка фермер собрал 6,5 центнеров клубники; с 1 га участка фермер собрал  7,2 центнера винограда.

Answer 2

Calculation of Grape and Strawberry Harvest

To calculate the amount of grapes and strawberries harvested by the farmer per hectare, we need to analyze the given information.

The farmer planted grapes on a 5-hectare plot and strawberries on a 3-hectare plot. On the second plot, the farmer also planted grapes on 3 hectares and strawberries on 5 hectares. The total harvest from the first plot was 55.5 tons, while the total harvest from the second plot was 54.1 tons of grapes and strawberries combined.

Let's calculate the harvest per hectare for grapes and strawberries separately.

# Grape Harvest Calculation

To calculate the grape harvest per hectare, we divide the total grape harvest by the total area planted with grapes.

The total grape harvest from the first plot is not provided, so we cannot calculate the grape harvest per hectare for the first plot.

For the second plot, the farmer planted grapes on 3 hectares and harvested 54.1 tons of grapes and strawberries combined. To calculate the grape harvest per hectare for the second plot, we divide the total grape harvest by the area planted with grapes.

Grape harvest per hectare on the second plot = Total grape harvest / Area planted with grapes on the second plot

Grape harvest per hectare on the second plot = 54.1 tons / 3 hectares

Grape harvest per hectare on the second plot = 18.03 tons/ha.

# Strawberry Harvest Calculation

To calculate the strawberry harvest per hectare, we divide the total strawberry harvest by the total area planted with strawberries.

The total strawberry harvest from the first plot is not provided, so we cannot calculate the strawberry harvest per hectare for the first plot.

For the second plot, the farmer planted strawberries on 5 hectares and harvested 54.1 tons of grapes and strawberries combined. To calculate the strawberry harvest per hectare for the second plot, we divide the total strawberry harvest by the area planted with strawberries.

Strawberry harvest per hectare on the second plot = Total strawberry harvest / Area planted with strawberries on the second plot

Strawberry harvest per hectare on the second plot = 54.1 tons / 5 hectares

Strawberry harvest per hectare on the second plot = 10.82 tons/ha.

Summary

Based on the given information, the farmer harvested approximately 18.03 tons of grapes per hectare from the second plot and approximately 10.82 tons of strawberries per hectare from the second plot.

Please note that the total grape and strawberry harvests from the first plot are not provided, so we cannot calculate the harvest per hectare for the first plot.

Let me know if there's anything else I can help you with!