Question

На день рождения подарили розы.Белых и желтых роз было 260 штук, желтых и красных роз было 270 штук , белых и красных 370 штук.Сколько роз было белого ,желтого и красного цвета ?.

Answer 1

Жёлтых-100шт
белых-110 шт.
Красных-100шт.

Answer 2

Calculation of the Number of Roses of Each Color

To determine the number of roses of each color, we can use a system of equations based on the given information.

Let's assign variables to represent the number of roses of each color: - Let x represent the number of white roses. - Let y represent the number of yellow roses. - Let z represent the number of red roses.

Based on the given information, we have the following equations:

1. "White and yellow roses totaled 260": - Equation 1: x + y = 260.

2. "Yellow and red roses totaled 270": - Equation 2: y + z = 270.

3. "White and red roses totaled 370": - Equation 3: x + z = 370.

To solve this system of equations, we can use various methods, such as substitution or elimination. Let's use the elimination method to find the values of x, y, and z.

Solving the System of Equations

To eliminate one variable, we can subtract Equation 1 from Equation 3:

(Equation 3) - (Equation 1): (x + z) - (x + y) = 370 - 260 z - y = 110

Now, we have a new equation: - Equation 4: z - y = 110

Next, we can add Equation 2 to Equation 4:

(Equation 2) + (Equation 4): (y + z) + (z - y) = 270 + 110 2z = 380

Simplifying the equation, we find: 2z = 380 z = 190

Now that we have the value of z, we can substitute it back into Equation 2 to find the value of y:

Equation 2: y + z = 270 y + 190 = 270 y = 270 - 190 y = 80

Finally, we can substitute the values of y and z into Equation 1 to find the value of x:

Equation 1: x + y = 260 x + 80 = 260 x = 260 - 80 x = 180

Answer:

Therefore, the number of roses of each color is as follows: - White roses: 180 - Yellow roses: 80 - Red roses: 190

Please let me know if there is anything else I can help you with!