Question

Каждому выпускнику школы решили подарить по одинаковому букету цветов. для этого купили 114 гвоздик Когда в каждый букет добавили ещё по 2 гвоздики, то там оказалось 5 цветков. Сколько выпускников было в школе?

Answer 1

Пусть букетов (и выпускников) было x, тогда...
5x-2x=114
3x=114
x=114/3
x=38
Ответ: 38 выпускников

Answer 2

Problem Analysis

We are given that each graduate of a school is to receive an identical bouquet of flowers. The school purchased 114 carnations and when 2 additional carnations were added to each bouquet, there were 5 flowers left. We need to determine the number of graduates in the school.

Solution

Let's assume that there are x graduates in the school. Since each graduate receives an identical bouquet, the total number of carnations used will be equal to the number of graduates multiplied by the number of carnations in each bouquet.

According to the given information, when 2 additional carnations were added to each bouquet, there were 5 flowers left. This means that the total number of carnations used is 5 more than the number of carnations in the bouquets.

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

x * (number of carnations in each bouquet) + 5 = total number of carnations used

We know that the total number of carnations used is 114, and the number of carnations in each bouquet is the original number plus 2. Let's solve the equation to find the value of x.

x * (x + 2) + 5 = 114

Simplifying the equation:

x^2 + 2x + 5 = 114

Rearranging the equation:

x^2 + 2x - 109 = 0

Now we can solve this quadratic equation to find the value of x.

Using the quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = 2, and c = -109.

Calculating the discriminant: b^2 - 4ac = 2^2 - 4(1)(-109) = 4 + 436 = 440

Since the discriminant is positive, we have two real solutions for x.

Using the quadratic formula:

x = (-2 ± sqrt(440)) / 2

Simplifying:

x = (-2 ± 20.976) / 2

Calculating the two possible values of x:

x1 = (-2 + 20.976) / 2 = 18.976 / 2 = 9.488

x2 = (-2 - 20.976) / 2 = -22.976 / 2 = -11.488

Since the number of graduates cannot be negative, we discard the negative solution.

Therefore, the number of graduates in the school is approximately 9.

Answer

There were approximately 9 graduates in the school.