They Divide Nicely

Algebra Level 1

182 sweets are equally divided among a certain number of children at a party. If the number of sweets each child receives is one more than the number of children, find the number of children at the party.


The answer is 13.

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David Agustinus by David Agustinus , 21, Sweden

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3 solutions

Hung Woei Neoh
Apr 21, 2016

Let the number of children be x x . The number of candy each child gets is x + 1 x+1

Therefore, we have the equation:

182 x = x + 1 182 = x ( x + 1 ) x 2 + x − 182 = 0 ( x + 14 ) ( x − 13 ) = 0 x = − 14 , 13 \dfrac{182}{x} = x+1\\ 182 = x(x+1)\\ x^2 + x - 182 = 0\\ (x + 14)(x - 13) = 0\\ x=-14, 13

Since we know that x > 0 x>0 , the number of children is x = 13 \boxed{x=13}

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I use the same method

Jason Chrysoprase - 5 years, 1 month ago
Whitney Clark
May 5, 2016

They were integers, so I guessed-and-checked.

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Abhay Tiwari
Apr 20, 2016

A simple multiplication will be enough to get the answer:

13 × 14 = 182 13×14=\boxed{182}

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But that would mean that you're testing values one by one until you get it

Hung Woei Neoh - 5 years, 1 month ago

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Yes I was testing the values but not one by one.

The number of candies given to a child is one greater than the number of children.

So that means ( n ) × ( n + 1 ) = 182. (n)×(n+1)=182.

Now think of the two numbers with this result.

It is obvious that, they cannot be greater than 15 as 15×16=240.

And cannot be less than 10 as 10×11=121.

This can be applied for smaller numbers, but for larger numbers we will have to go through the conventional way only(like you did).

Abhay Tiwari - 5 years, 1 month ago

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There is one more method, just factorise 182.

182 ⇒ 13 × 7 × 2 ⇒ 13 × 14 182 \Rightarrow 13 \times 7 \times 2 \Rightarrow 13 \times 14

There we get our answer!

Yash Jain - 5 years, 1 month ago

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@Yash Jain – Yes, this looks good. :)

Abhay Tiwari - 5 years, 1 month ago

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@Abhay Tiwari – Kinda similarly I checked integers, but to narrow the field, i took the sqrt(182) and got 13.5, so the first numbers I checked were 13 and 14 and it worked!

Connor Jennison - 5 years, 1 month ago

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@Connor Jennison – Ya, this is good too, gets you the idea for the values, good one :)

Abhay Tiwari - 5 years, 1 month ago

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