Question

16. The students of a class arranged a picnic. Each student contributed as
the number of students in the class. If the total contribution is 1156, find
the class.
​

Answer 1

Answer:

Let the number of students be x.

Hence, the amount contributed by each student is Rs x.

Total amount contributed -> x×x=x^2=1156

1156=2*2*17*17

X= Square root 1156 =2*17=34

So the strength of class is 34.

Answer 2

Answer:

Given Information:-

• Each student contributed as the number of students in the class.
• Total contribution was 1156 currency.

To Find:-

Total number of students in class.

________________...

Let the number of students in the class be = $x$

∴ The contribution by one student become = $x$

(∵ The contribution was equal to the number of students.)

Total contribution was = $1156$

$\tt{\underline{According \ to \ the \ question:-}}$

$x \times x = 1156$

(Formation of a suitable equation to find the value of the variable)

$\implies {x}^{2} = 1156$

(∵ x × x = x²)

$\implies x = \sqrt{1156}$

(∵ The value of x would be root over of the constant term in the RHS)

$\implies x = \sqrt{ \underline{2 \times 2} \times \underline{17 \times 17 }}$

(Through prime factorisation, we have divided 1156 into many prime numbers; we have grouped the same numbers in pairs)

$\implies x = \sqrt{{(2)}^{2} \times {(17)}^{2} }$

(More modifications inside the radical sign)

$\implies x = 2 \times 17$

(Taken out the numbers from the radical sign which were having 2 as their exponent; the exponent becomes 1 after coming out from the radical sign)

$\implies x = 34$

(Product of 2 and 7; ANSWER)

__________________...

Required Answer:-

Since, the contribution was equal to the number if students, therefore we can conclude that the number of students in the class was 34.