Question

in a class with a certain number of students if one student weighing 50 kg is added then the average weight of the class increases by 1 kg. if one more student weighing 50 kg is added then the average weight of the class increases by 1.5 kg over the original average. what is the original average weight (in kg) of the class? 46 4 2 47

Answer 1

The correct option is:  47 kg.

Explanation

Suppose, the original average weight of the class was  $x$ kg.                                   and the number of students in the class in starting was  $y$

So, the total weight of the class was:  $(xy)$ kg.

If one student weighing 50 kg is added then the average weight of the class increases by 1 kg. So, the first equation will be......

$\frac{xy+50}{y+1}= x+1\\ \\ xy+50=(x+1)(y+1)\\ \\ xy+50= xy+x+y+1\\ \\ x+y=49 ........................................... (1)$

If one more student weighing 50 kg is added then the average weight of the class increases by 1.5 kg over the original average. So, the second equation will be.....

$\frac{xy+50+50}{y+1+1}= x+1.5\\ \\ \frac{xy+100}{y+2}=x+1.5\\ \\ xy+100=(x+1.5)(y+2)\\ \\ xy+100= xy+2x+1.5y+3\\ \\ 2x+1.5y=97 .................................. (2)$

Isolating $y$ in left side in the first equation.....

$y=49-x$

Now, we will plug this  $y=49-x$ into equation (2). So, we will get......

$2x+1.5(49-x)=97\\ \\ 2x+73.5-1.5x=97\\ \\ 0.5x=97-73.5\\ \\ 0.5x=23.5\\ \\ x=\frac{23.5}{0.5}=47$

So, the original average weight of the class is  47 kg.

Answer 2

Let number of students in the class be n

Average weight of the class be x

Total weight of the class = nx

If one student (50 kg) joins, comparing total weight of the class

(n+1)(x+1) = nx + 50

If second student (50 kg) joins, comparing total weight of the class

(n+2)(x+1.5) = nx + 100

Solving the equations we get

n + x = 49 - (1)

1.5n + 2x = 97 - (2)

From (1), n = 49 - x

Putting in (2) we get

73.5 + 0.5 x = 97  

0.5x = 23.5 or x = 47