Question

Помидор и огурец вместе весят столько же,сколько морковь и свекла.Помидор вместе с морковью весят меньше,чем огурец со свеклой,а морковь вместе с огурцом весят меньше,чем помидор со свеклой.Что из овощей является самым тяжелым?

Answer 1

Analysis and Solution

To determine which vegetable is the heaviest, let's assign variables to the weights of the vegetables. Let's say the weight of the tomato is T, the weight of the cucumber is C, the weight of the carrot is M, and the weight of the beetroot is S.

From the given information, we can deduce the following equations:

1. T + C = M + S (The weight of the tomato and cucumber together is equal to the weight of the carrot and beetroot together). 2. T + M < C + S (The weight of the tomato and carrot together is less than the weight of the cucumber and beetroot together). 3. M + C < T + S (The weight of the carrot and cucumber together is less than the weight of the tomato and beetroot together).

We need to find the vegetable with the highest weight, so we can compare the weights of the different vegetables.

Let's solve these equations to find the weight of each vegetable.

From equation 1, we can rewrite it as T - M = S - C.

From equation 2, we can rewrite it as T - C < S - M.

From equation 3, we can rewrite it as M - C < S - T.

Combining these equations, we have:

T - M = S - C

T - C < S - M

M - C < S - T

Now, let's analyze the given information and solve the equations to find the heaviest vegetable.

Solution:

From the given information, we have:

1. T + C = M + S 2. T + M < C + S 3. M + C < T + S

Let's solve these equations step by step:

From equation 1, we have T - M = S - C.

From equation 2, we have T - C < S - M.

From equation 3, we have M - C < S - T.

Now, let's analyze the equations:

1. T - M = S - C: This equation tells us that the difference between the weight of the tomato and the weight of the carrot is equal to the difference between the weight of the beetroot and the weight of the cucumber.

2. T - C < S - M: This equation tells us that the difference between the weight of the tomato and the weight of the cucumber is less than the difference between the weight of the beetroot and the weight of the carrot.

3. M - C < S - T: This equation tells us that the difference between the weight of the carrot and the weight of the cucumber is less than the difference between the weight of the beetroot and the weight of the tomato.

From these equations, we can conclude that the weight of the tomato is less than the weight of the beetroot, and the weight of the cucumber is less than the weight of the carrot.

Therefore, the beetroot is the heaviest vegetable among the given options.

Please let me know if I can help you with anything else.