Question

За 1 шоколадку и 2пачки печенья заплатили 130руб. За 1 шок. и 4 пачки печенья заплатили 230 руб. Верно ли утверждение,что 2 шоколадки дешевли 2 пачек печенья?

Answer 1

230-130=100 (руб ) - 2 пачки печенья
130-100=30 (руб) 1 шоколадки
30×2=60(руб)- 2шоколадки
Всё верно.

Answer 2

Х стоит шоколадка
у стоит пачка печенья
(х+4у)- (х+2у)=230-130
х+4у-х-2у=100
2у=100
у=50 стоит печенье
130-(2*50)=30 р стоит шоколадка
2*30<2*50
утверждение верно

Answer 3

Problem Analysis

We are given two scenarios of purchasing chocolate and cookies and the corresponding prices. We need to determine if the statement that "2 chocolates are cheaper than 2 packs of cookies" is true.

Solution

To solve this problem, we can set up a system of equations based on the given information and then solve for the prices of the chocolate and cookies.

Let's assume the price of one chocolate is x rubles and the price of one pack of cookies is y rubles.

From the first scenario, we know that: - 1 chocolate + 2 packs of cookies = 130 rubles

From the second scenario, we know that: - 1 chocolate + 4 packs of cookies = 230 rubles

We can set up the following equations based on the given information:

Equation 1: x + 2y = 130 (from the first scenario) Equation 2: x + 4y = 230 (from the second scenario)

To solve this system of equations, we can use the method of substitution or elimination.

Let's solve it using the method of substitution:

From Equation 1, we can express x in terms of y: x = 130 - 2y

Substituting this value of x into Equation 2, we get: (130 - 2y) + 4y = 230

Simplifying the equation: 130 + 2y = 230 2y = 100 y = 50

Now, substituting the value of y back into Equation 1, we get: x + 2(50) = 130 x + 100 = 130 x = 30

Therefore, the price of one chocolate is 30 rubles and the price of one pack of cookies is 50 rubles.

To determine if the statement that "2 chocolates are cheaper than 2 packs of cookies" is true, we can compare the total prices:

- 2 chocolates: 2 * 30 = 60 rubles - 2 packs of cookies: 2 * 50 = 100 rubles

Since 60 rubles is less than 100 rubles, we can conclude that 2 chocolates are indeed cheaper than 2 packs of cookies.

Conclusion

Based on the given information, we have determined that the statement "2 chocolates are cheaper than 2 packs of cookies" is true. The price of one chocolate is 30 rubles and the price of one pack of cookies is 50 rubles.