Datan asks you "Hey Yosief, I have a question for you, if I gives 4 chocolate bars to each child at my party, I will have 38 left. If I give 7 chocolate bars each, I will have 2 chocolate bars left. How many children were there at my birthday party?"

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Answer 1 · 2016-09-30T09:09:58

There were $12$ children at Datan's birthday party.

Le the number of children at Datan's birthday be $x$ .

If he gives $4$ chocolate bars to each child at his party i.e. in all $4xx x$ and he has $38$ left, he must be having

$4xx x+38=4x+38$ chocolate bars.

If Datan gives $7$ chocolate bars to each child at his party i.e. in all $7xx x$ and he has $2$ left, he must be having

$7xx x+2=7x+2$ chocolate bars.

Hence, as the two should be equal, we have $7x+2=4x+38$

or $7x+2-4x-2=4x+38-4x-2$

or $7x+cancel2-4x-cancel2=cancel(4x)+38-cancel(4x)-2$

i.e. $3x=36$ and hence $x=36/3=12$

There were $12$ children at Datan's birthday party.