Question

Помогите решить задачу В коробке 42 карандаша. Сколько карандашей каждого цвета, если зелёных и жёлтых 35 карандашей, а жёлтых красных 28 карандаше?

Answer 1

Составляем уравнение.
x - зелёные
y - жёлтые
z - красные

x + y = 35
y + z = 28
x + y + z = 42, значит z = 42 - x - y

y + z = 28, подставляем z: y + 42 - x - y = 28. y - y = 0, остаётся 42 - x = 28, значит 42 - 28 = x, то есть x = 14 (зелёных карандашей 14).

x + y = 35, подставляем x = 14: 14 + y = 35, значит y = 35 - 14 = 21 (жёлтых карандашей 21).

y + z = 28, подставляем y: 21 + z = 28, значит z = 28 - 21 = 7 (красных карандашей 7).

Проверяем: 14 + 21 + 7 = 42

Answer 2

Problem Analysis

We are given that there are a total of 42 pencils in a box. We also know that there are 35 green and yellow pencils combined, and 28 yellow and red pencils combined. We need to determine the number of pencils of each color.

Solution

Let's assume the number of green pencils is G, the number of yellow pencils is Y, and the number of red pencils is R.

From the given information, we can write the following equations: 1. G + Y = 35 (equation 1) 2. Y + R = 28 (equation 2) 3. G + Y + R = 42 (equation 3)

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

Subtracting equation 2 from equation 3, we get: (G + Y + R) - (Y + R) = 42 - 28 G = 14 (equation 4)

Substituting the value of G from equation 4 into equation 1, we get: 14 + Y = 35 Y = 35 - 14 Y = 21 (equation 5)

Substituting the value of Y from equation 5 into equation 2, we get: 21 + R = 28 R = 28 - 21 R = 7 (equation 6)

Therefore, the number of green pencils is 14, the number of yellow pencils is 21, and the number of red pencils is 7.

Answer

There are 14 green pencils, 21 yellow pencils, and 7 red pencils in the box.

Please let me know if you need any further assistance!

Answer 3

Problem Analysis

We are given that there are 42 pencils in a box. We also know that there are 35 green and yellow pencils combined, and 28 yellow and red pencils combined. We need to determine the number of pencils of each color.

Solution

Let's assume the number of green pencils is G, the number of yellow pencils is Y, and the number of red pencils is R.

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

1. G + Y = 35 (equation 1) 2. Y + R = 28 (equation 2) 3. G + Y + R = 42 (equation 3)

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

Adding equation 1 and equation 2, we get:

(G + Y) + (Y + R) = 35 + 28 G + 2Y + R = 63 (equation 4)

Subtracting equation 2 from equation 3, we get:

(G + Y + R) - (Y + R) = 42 - 28 G + Y = 14 (equation 5)

Now, we have two equations:

G + 2Y + R = 63 (equation 4) G + Y = 14 (equation 5)

Subtracting equation 5 from equation 4, we get:

(G + 2Y + R) - (G + Y) = 63 - 14 Y + R = 49 (equation 6)

Now, we have two equations:

Y + R = 49 (equation 6) G + Y = 14 (equation 5)

From equation 5, we can express G in terms of Y:

G = 14 - Y (equation 7)

Substituting equation 7 into equation 6, we get:

(14 - Y) + Y = 49 14 + Y = 49 Y = 49 - 14 Y = 35

Substituting the value of Y back into equation 5, we get:

G + 35 = 14 G = 14 - 35 G = -21

Since we cannot have a negative number of pencils, it means there is an error in the given information or the problem itself.

Therefore, it is not possible to determine the number of pencils of each color based on the given information.

Note: The given information leads to an inconsistent system of equations, which means there is no solution that satisfies all the equations simultaneously.

Conclusion

Based on the given information, it is not possible to determine the number of pencils of each color.