Question

Масса двух одинаковых апельсинов и одного лимона равна 400 г,а масса таких де двух апельсинов и трёх лимонов--- 600г.Какова масса одного апельсина и какова -- одного лимона??

Answer 1

По условию задачи 2*А + 1*Л = 400,   2*А+ 3*Л= 600, где А-апельсин, Л-лимон. 
(2А+3Л)-(2А+Л)= 600-400
3Л-Л=200
2Л=200
Л=100 г   масса одного лимона 
2А=400-Л
2А=400-100
2А=300
А=150 г   масса одного апельсина

Answer 2

Problem Analysis

We are given the information that the combined weight of two oranges and one lemon is 400 grams, and the combined weight of two oranges and three lemons is 600 grams. We need to find the weight of one orange and the weight of one lemon.

Solution

Let's assume the weight of one orange is x grams and the weight of one lemon is y grams.

According to the given information, we can set up the following equations:

Equation 1: 2x + y = 400 grams Equation 2: 2x + 3y = 600 grams

To solve these equations, we can use a method called substitution.

Solving the Equations

We can solve Equation 1 for y and substitute it into Equation 2:

From Equation 1: y = 400 - 2x

Substituting this value of y into Equation 2:

2x + 3(400 - 2x) = 600

Simplifying the equation:

2x + 1200 - 6x = 600 -4x + 1200 = 600 -4x = -600 x = 150

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

2(150) + y = 400 300 + y = 400 y = 100

Answer

Therefore, the weight of one orange is 150 grams and the weight of one lemon is 100 grams.

Verification

Let's verify our solution by substituting the values of x and y back into the original equations:

Equation 1: 2x + y = 400 2(150) + 100 = 400 300 + 100 = 400 400 = 400 (True)

Equation 2: 2x + 3y = 600 2(150) + 3(100) = 600 300 + 300 = 600 600 = 600 (True)

Our solution satisfies both equations, so it is correct.