Question

2 упаковки конфет и 2 упаковки орехов весят 1.1кг. 5 упаковок конфет и 3 упаковки орехов весят 2.15 кг. а)Сколько граммов весит одна упаковка конфет? в)Сколько граммов весит одна упаковка орехов?

Answer 1

{ 2К + 2О = 1,1
{ 5К + 3О = 2,15
1 уравнение делим на 2
{ К + О = 0,55
{ 5К + 3О = 2,15
Подставляем 1 уравнение во 2 уравнение
5К + 3О = 2К + 3К + 3О = 2К + 3*0,55 = 2К + 1,65 = 2,15
2К = 2,15 - 1,65 = 0,5
К = 0,25 кг весит упаковка конфет.
О = 0,55 - 0,25 = 0,3 кг весит упаковка орехов.

Answer 2

Problem Analysis

We are given the weights of two packages of candies and two packages of nuts, as well as the weights of five packages of candies and three packages of nuts. We need to find the weight of one package of candies and one package of nuts.

Solution

Let's assume the weight of one package of candies is x grams and the weight of one package of nuts is y grams.

From the given information, we can set up the following equations:

Equation 1: 2x + 2y = 1.1 kg (1100 grams) Equation 2: 5x + 3y = 2.15 kg (2150 grams)

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

Multiplying Equation 1 by 5 and Equation 2 by 2, we get:

Equation 3: 10x + 10y = 5.5 kg (5500 grams) Equation 4: 10x + 6y = 4.3 kg (4300 grams)

Subtracting Equation 4 from Equation 3, we get:

4y = 1200 grams

Dividing both sides by 4, we find:

y = 300 grams

Now, we can substitute the value of y into Equation 1 to find x:

2x + 2(300) = 1100 grams 2x + 600 = 1100 grams 2x = 500 grams x = 250 grams

Therefore, one package of candies weighs 250 grams and one package of nuts weighs 300 grams.

Answer

a) One package of candies weighs 250 grams. b) One package of nuts weighs 300 grams.