Question

В викторине приняли участие 3 школы . количество учащихся первой школы 3/7 от учащихся 2 школы ,а количество учащихся 3 школы оставило 0,8 от учащихся 2 школы . сколько человек участвовало в викторине от каждой школы , если общее число участников составило 78 человек

Answer 1

Х-человек из 2й школы
3/7х-человек из 1й школы
0,8х-человек из 3й школы

х+3/7х+0,8х=78
х+3/7х+8/10х=78
х+3/7х+4/5х=78
35/35х+15/35х+28/35х=78
78/35х=78
х=78:78/35=78*35/78=35-человек из 2й школы
3/7*35=15-человек из 1й школы
0,8*35=28-человек из 3й школы

Answer 2

Problem Analysis

We are given that three schools participated in a quiz, and we need to determine the number of participants from each school. We are given the following information: - The number of students from the first school is 3/7 of the number of students from the second school. - The number of students from the third school is 0.8 times the number of students from the second school. - The total number of participants in the quiz is 78.

Let's solve this problem step by step.

Solution

Let's assume: - The number of students from the first school is x. - The number of students from the second school is y. - The number of students from the third school is z.

From the given information, we can write the following equations: 1. The number of students from the first school is 3/7 of the number of students from the second school: x = (3/7)y. 2. The number of students from the third school is 0.8 times the number of students from the second school: z = 0.8y. 3. The total number of participants in the quiz is 78: x + y + z = 78.

We can solve these equations to find the values of x, y, and z.

Solving the Equations

Let's substitute the value of x from equation 1 into equation 3: (3/7)y + y + z = 78.

Now, let's substitute the value of z from equation 2 into the above equation: (3/7)y + y + 0.8y = 78.

Simplifying the equation: (3/7 + 1 + 0.8)y = 78.

Combining the fractions: (3/7 + 7/7 + 8/10)y = 78.

Finding a common denominator: (30/70 + 70/70 + 56/70)y = 78.

Combining the fractions: (30 + 70 + 56)/70y = 78.

Simplifying the equation: 156/70y = 78.

Cross-multiplying: 156y = 78 * 70.

Simplifying: 156y = 5460.

Dividing both sides by 156: y = 5460 / 156.

Calculating: y = 35.

Now, let's substitute the value of y into equation 1 to find x: x = (3/7) * 35.

Calculating: x = 15.

Finally, let's substitute the value of y into equation 2 to find z: z = 0.8 * 35.

Calculating: z = 28.

Answer

Therefore, the number of participants from each school is as follows: - The first school: 15 students. - The second school: 35 students. - The third school: 28 students.

Please let me know if you need any further assistance!