Question

До новорічного свята треба було виготовити 48 гирлянд.Цю роботу доручили кільком учням.Якби учнів було на 2 більше,то гирлянд кожному довелося б зробити на 4 менше.Скільки було учнів і скільки гирлянд виготовив кожен з них?

Answer 1

6 учнів 8 гірлянд мав кожен зробити

Answer 2

Problem Analysis

We are given that there were 48 garlands to be made for the New Year's holiday. Several students were assigned this task. If there were 2 more students, each student would have had to make 4 fewer garlands. We need to determine the number of students and the number of garlands each student made.

Solution

Let's assume that initially, there were x students assigned to make the garlands. Each student would have made 48/x garlands.

According to the given information, if there were 2 more students, each student would have had to make 4 fewer garlands. This can be expressed as:

48/(x+2) = 48/x - 4

To solve this equation, we can cross-multiply:

48x = 48(x+2) - 4x(x+2)

Simplifying the equation:

48x = 48x + 96 - 4x^2 - 8x

Combining like terms:

0 = -4x^2 - 8x + 96

Dividing the equation by -4:

0 = x^2 + 2x - 24

Factoring the quadratic equation:

0 = (x + 6)(x - 4)

Setting each factor equal to zero:

x + 6 = 0 or x - 4 = 0

Solving for x:

x = -6 or x = 4

Since the number of students cannot be negative, we discard the solution x = -6. Therefore, the number of students is x = 4.

To find the number of garlands each student made, we substitute x = 4 into the initial equation:

48/4 = 12

Therefore, each student made 12 garlands.

Answer

There were 4 students and each student made 12 garlands.