Question

ii) Rajnana wants to distribute 450 oranges among some students. It 15 students were
each would get 2 organges less. Find the number of students.
​

Answer 1

Correct Question

Rajnana wants to distribute 450 oranges among some students. If 15 students were more each would get 2 oranges less. Find the number of students.

Answer

Total number of students is 51

Explanation

Total number of oranges = 450

Let us assume that there are total x students.

So, number of oranges each student will get = 450/x

If there are15 students more then,

Total number of students = x + 15

So, number of oranges students will get = 450/(x + 15)

If 15 students were more each would get 2 oranges less.

Means, 450/x - 2

According to question,

⇒ 450/(x + 15) = 450/x - 2

⇒ 450/(x + 15) - 450/x = -2

⇒ 450/x - 450/(x + 15) = 2

⇒ 450 × [(1/x - 1)/(x + 15)] = 2

⇒ 450 × [(x + 15 - x)/(x² + 15x)] = 2

⇒ 450 × (15)/(x² + 15x) = 2

⇒ 450(15) = 2(x² + 15x)

⇒ 225(15) = x² + 15x

⇒ 3375 = x² + 15x

⇒ x² + 15x - 3375 = 0

The above equation is in the form ax² + bx + c = 0. Where, a = 1, b = 15 and c = -3375

Now, solve it using the quadratic formula.

$\sf{x \: = \: \frac{ - b \pm \sqrt{( {b) }^{2} - 4ac} }{2a} }$

$\sf{x \: = \: \frac{ - 15 \pm \sqrt{( {15) }^{2} - 4(1)(-3375)} }{2(1)} }$

$\sf{x \: = \: \frac{ - 15 \pm \sqrt{225 +13500} }{2(1)} }$

$\sf{x \: = \: \frac{ - 15 \pm \sqrt{13725} }{2} }$

$\sf{x\:=\:\frac{-15 \pm 117}{2}}$

$\sf{x\:=\:\frac{-15+117}{2}}$, $\sf{x\:=\:\frac{-15-117}{2}}$

$\sf{x\:=\:+51, -66}$

(Students can be negative. So, the negative one neglected)

Therefore, Number of students is 51.

Answer 2

☺heya

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