Question

В зрительном зале маленького театра 100 мест.В день премьеры спектакля все билеты были проданы на общую сумму 1000 рублей.Билет для мужчин стоит 50 рублей,для женщин 20 рублей, а для детей 1 рубль.Сколько мужчин женщин и детей было на премьере? подскажите пожалуйста

Answer 1

Я уже отвечал на такой вопрос, это можно сделать методом подбора и тогда получается:
3-мужчины
40-женщин
50-детей

Answer 2

Problem Analysis

We are given the following information: - The theater has 100 seats. - All tickets for the premiere of the play were sold for a total of 1000 rubles. - Tickets for men cost 50 rubles, tickets for women cost 20 rubles, and tickets for children cost 1 ruble.

We need to determine the number of men, women, and children who attended the premiere.

Solution

Let's assume the number of men, women, and children who attended the premiere are represented by variables `m`, `w`, and `c`, respectively.

We can set up the following equations based on the given information: 1. The total number of tickets sold is equal to the sum of tickets sold to men, women, and children: `m + w + c = 100` (equation 1) 2. The total revenue from ticket sales is equal to the sum of revenue from tickets sold to men, women, and children: `50m + 20w + 1c = 1000` (equation 2)

We can solve these equations to find the values of `m`, `w`, and `c`.

Solution Steps

1. Solve equation 1 for `m`: `m = 100 - w - c` 2. Substitute the value of `m` in equation 2: `50(100 - w - c) + 20w + c = 1000` Simplify the equation: `5000 - 50w - 50c + 20w + c = 1000` Combine like terms: `-30w - 49c = -4000` (equation 3) 3. Solve equation 3 for `c`: `c = (30w + 4000) / 49` 4. Since `c` must be a whole number, we can try different values of `w` and check if `c` is an integer. - Let's start with `w = 0`: `c = (30(0) + 4000) / 49 = 4000 / 49 ≈ 81.63` Since `c` is not an integer, `w = 0` is not a valid solution. - Let's try `w = 1`: `c = (30(1) + 4000) / 49 = 4030 / 49 ≈ 82.24` Again, `c` is not an integer, so `w = 1` is not a valid solution. - We can continue trying different values of `w` until we find a valid solution.

Let's calculate the values of `m`, `w`, and `c` using the above steps.