There would be 12 people at the party!
In general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1+2+3+ ... + n.
Since this sum is n(n+1)/2, we need to solve the equation n(n+1)/2 = 66.
This is the quadratic equation n2+ n -132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party.
Since 66 is a relatively small number, you can also solve this problem with a hand calculator. Add 1 + 2 = + 3 = +... etc. until the total is 66. The last number that you entered (11) is n.
Hope this helps!
Answer:
222
Step-by-step explanation:
Let me know if it is correct!
Steps to solve:
3x + 2 = 8
~Subtract 2 to both sides
3x = 6
~Divide 3 to both sides
x = 2
Best of Luck!
15x - 30 = 105 is the mathematical statement
