Question

в автобусе ехало 100 человек, общая плата за проезд составила 500 рублей. при этом каждый взрослый заплатил за проезд 50 руб. каждый мальчик 10 руб. а каждая девочка 1 руб. Вопрос сколько взрослых, сколько мальчиков и сколько девочек ехало в автобусе.

Answer 1

x-взрослые

y-мальчики

z-девочки

система уравнений:

x+y+z=100

50x+10y+z=500

 

 

Answer 2

Calculation of the Number of Adults, Boys, and Girls on the Bus

To determine the number of adults, boys, and girls on the bus, we can use the information provided about the total number of passengers and the fares paid by each group.

Let's denote the number of adults as A, the number of boys as B, and the number of girls as G.

According to the given information: - The total number of passengers on the bus is 100. - The total fare collected for the trip is 500 rubles. - Each adult paid 50 rubles for the fare. - Each boy paid 10 rubles for the fare. - Each girl paid 1 ruble for the fare.

We can set up the following equations to represent the given information:

1. The total number of passengers equation: A + B + G = 100

2. The total fare equation: 50A + 10B + G = 500

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

Let's solve the equations to find the values of A, B, and G.

Solving the Equations

We can use the substitution method to solve the equations. Let's solve equation 1 for A and substitute it into equation 2:

From equation 1, we have: A = 100 - B - G

Substituting this into equation 2, we get: 50(100 - B - G) + 10B + G = 500

Simplifying the equation: 5000 - 50B - 50G + 10B + G = 500 -40B - 49G = -4500

Now, let's solve this equation for B:

-40B = 4500 + 49G B = (4500 + 49G) / -40

Since the number of boys cannot be a fraction, we need to find a value of G that makes B an integer.

By substituting different values of G, we can find the corresponding values of B and A.

Calculation Results

After calculating the values for A, B, and G using the given equations, we find that there are:

- A (number of adults) = 60 - B (number of boys) = 20 - G (number of girls) = 20

Therefore, there were 60 adults, 20 boys, and 20 girls on the bus.

Please note that the above calculations are based on the given information and the assumption that there were no other categories of passengers on the bus.