Question

2 группы зрителей за одинаковые по цене билеты в цирк заплатили 1800 руб. и 3050 руб. Сколько стоил один билет если в одной группе было на 5 человек больше чем в другой закончи схематический чертеж

Answer 1

Calculation of Ticket Price and Group Sizes

To find the cost of one ticket and the sizes of the two groups, we can set up a system of equations based on the given information.

Let's assume that the cost of one ticket is x rubles. We are given that two groups of spectators paid a total of 1800 rubles and 3050 rubles, respectively.

We can set up the following equations:

Equation 1: x * (number of people in Group 1) = 1800 Equation 2: x * (number of people in Group 2) = 3050

We are also given that there were 5 more people in Group 1 than in Group 2.

Let's solve this system of equations to find the cost of one ticket and the sizes of the two groups.

Solving the System of Equations

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

From Equation 1, we can express the number of people in Group 1 in terms of x:

Number of people in Group 1 = 1800 / x

From Equation 2, we can express the number of people in Group 2 in terms of x:

Number of people in Group 2 = 3050 / x

We are given that the number of people in Group 1 is 5 more than the number of people in Group 2. So we can set up the following equation:

Number of people in Group 1 = Number of people in Group 2 + 5

Substituting the expressions for the number of people in Group 1 and Group 2, we have:

1800 / x = 3050 / x + 5

Now, let's solve this equation to find the value of x.

Solving the Equation for x

To solve the equation 1800 / x = 3050 / x + 5, we can cross-multiply:

1800 * x = (3050 + 5 * x) * x

Simplifying the equation:

1800 * x = 3050 * x + 5 * x^2

Rearranging the equation:

5 * x^2 + 3050 * x - 1800 * x = 0

5 * x^2 + 1250 * x = 0

Factoring out x:

x * (5 * x + 1250) = 0

From this equation, we can see that x = 0 or x = -1250 / 5. Since the cost of a ticket cannot be zero or negative, we can disregard x = 0.

Therefore, the cost of one ticket is x = -1250 / 5 = -250 rubles.

However, it is important to note that a negative ticket price does not make sense in this context. It is likely that there was an error in the given information or calculation. Please double-check the values provided.

Schematic Diagram

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