Question

On a hot summer day in the RSM camp at Sunapee, students had to do several activities in a row. For the first activity, they were split into pairs and Ms. Eleonora prepared a bottle of iced tea for each pair. The next activity was for groups of three students and Ms. Eleonora gave each group a bottle of Pepsi. The last activity needed groups of four and each group got a bottle of lemonade. Also, each student got an individual bottle of water. How many kids took part in these activities if, at the end of the day, 50 empty bottles were collected? (No bottles were taken away)

Answer 1

Answer:-

Let the number of bottles given to each individual be a, no. bottles given to pairs of students be b, no. of bottles given to groups of 3 individuals be c, and the no. of bottles given to group of four individuals be d .

A.T.Q.

$a + b + c + d = 50 \:$

$\implies \: a + \frac{a}{2} + \frac{a}{3} + \frac{a}{4} = 50$

$\frac{12a + 6a + 4a + 3a}{12} = 50 \\ \\ \frac{25a}{12} = 50\\ \\ a = 24$

Hence, 24 kids took part in the activities.

Answer 2

Answer :-

Let the number of bottles given to each individual be a, no. bottles given to pairs of students be b, no. of bottles given to groups of 3 individuals be c, and the no. of bottles given to group of four individuals be d .

This can also be represented as follows :-

$\implies \: a = 1 \\ \\ \implies \: b = \frac{a}{2} \\ \\ \implies \: c = \frac{a}{3} \\ \\ \implies \: d = \frac{a}{4}$

A.T.Q.

$a + b + c + d = 50 \:$

$\implies \: a + \frac{a}{2} + \frac{a}{3} + \frac{a}{4} = 50$

LCM of 1, 2, 3, and 4 is 12

$\frac{12a + 6a + 4a + 3a}{12} = 50 \\ \\ \frac{25a}{12} = 50\\ \\ a = \frac{50 \times 12}{25} \\ \\ a = 24$

Therefore, 24 kids took part in the activities.

Hope it helps ♡~