Question

hello mate....❤️



At a party, everyone shook hands with everybody else. There were 45 handshakes. How many people were at the party?
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Answer 1

${\huge {\mathfrak {Answer :-}}}$

We have,

⚠️ In a party, Everyone shook hands with everybody else.

⚠️ There were total 45 handshakes.

⚠️ Number of people at the party = ?

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Let, the number of people at the party be $x$.

◾By condition,

${} [ x(x - 1) ] / 2 = 45.$

${} x^2 - x = 90$

${} x^2 - x - 90 = 0$

${} x^2 - 10x + 9x - 90 = 0$

${} x(x - 10) + 9(x - 10) = 0$

${} (x + 9)(x - 10) = 0$

${} x = 10, - 9$

➡️ Since, the number of people can't be in negative.

So , $x$ = 10.

✨ Hence, the number of people at the party were 10.

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$\bold {EXPLANATION}$

Look, it is difficult for me to explain how I solved this sum, but I'll try my best to.

To solve this sum, I have taken concept form the IPL ( Indian Premier League ).

⚠️ In IPL, there are 8 teams that face off every team else 2 times. This accounts for a total 56 matches.

⚠️ Teams face off 2 times = 56 matches. So, if the teams face off 1 time = 56/2 = 28 matches.

⚠️ 8 teams face off every team else that accounts for 28 matches.

⚠️ Now we have, 28 = 56/2 = (8*7)/2 = [ 8(8 - 1) ] / 2 = 28.

➡️ 8(8 - 1) / 2 = 28 ⬅️

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Ok, now using it and verifying the answer in the previous one.

We have, 10(10 - 1) /2

= 10 * 9 /2

= 45.

Hence, verified.

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✨HOPE THIS HELPS ✨