Question

С трёх участков земли собрали 156 ц картофеля. С первого участка собрали х ц картофеля, со второго — столько же, сколько с первого, а с третьего — на 12 ц больше, чем с каждого из первых двух. 1) Запишите выражения для следующих величин: • масса картофеля, собранного со второго участка; • масса картофеля, собранного с третьего участка; • масса картофеля, собранного с трёх участков. 2) Сопоставьте полученные выражения с условием задачи и найдите равные величины. Ответ запишите в виде уравнения. 3) Какую величину вы найдёте, если решите полученное уравнение? Решите его. 4) Сколько картофеля собрали со второго и сколько — с третьего участка?

Answer 1

1) х- со 2 участка . т.к. урожай такой же. как и на 1-м участке
   х+12- с 3 участка
х+х+(х+12)- с трех участков
2) х+х+(х+12)=156
3х=144
х=144:3
х=48
По 48 ц картофеля собрали с 1 и второго участков, а с 3 - 48+12=60ц
Проверка: 48+48+60=156 (верно)

Answer 2

Question interpretation: The question is asking for a detailed solution to a problem involving three plots of land and the amount of potatoes harvested from each plot. The total amount of potatoes harvested from all three plots is 156 c. From the first plot, they harvested x c of potatoes. From the second plot, they harvested the same amount as the first plot, and from the third plot, they harvested 12 c more than from each of the first two plots. The question asks to: 1. Write expressions for the following quantities: - The mass of potatoes harvested from the second plot - The mass of potatoes harvested from the third plot - The mass of potatoes harvested from all three plots 2. Compare the obtained expressions with the conditions of the problem and find equal quantities. Write the answer in the form of an equation. 3. Determine the unknown quantity by solving the obtained equation. 4. Calculate the amount of potatoes harvested from the second and third plots.

Solution: Let's solve the problem step by step.

1. Expressions for the quantities: - Mass of potatoes harvested from the second plot: x c - Mass of potatoes harvested from the third plot: x c + x c + 12 c = 2x + 12 c - Mass of potatoes harvested from all three plots: x c + x c + 2x + 12 c = 4x + 12 c

2. Comparison and equation: According to the problem, the total mass of potatoes harvested from all three plots is 156 c. So we can write the equation: 4x + 12 c = 156 c

3. Solving the equation: To solve the equation, we need to isolate x. Let's start by subtracting 12 c from both sides of the equation: 4x = 156 c - 12 c 4x = 144 c Now, divide both sides of the equation by 4: x = 144 c / 4 x = 36 c

4. Calculating the amount of potatoes harvested from the second and third plots: Mass of potatoes harvested from the second plot: x = 36 c Mass of potatoes harvested from the third plot: 2x + 12 c = 2(36 c) + 12 c = 72 c + 12 c = 84 c

Therefore, they harvested 36 c of potatoes from the second plot and 84 c of potatoes from the third plot.