Charmaine= x
William=x+3
3 times Charmaine = 3x
2times William = 2x+6
5x+6=76
5x=76-6
5x=70
X=14
Charmaine is 14
William is 3 years older so is 17
Check:
17x2= 34
14x3=42
34+42=76
So Charmaine is 14
William is 17
So even postive integers are by defention in form 2k where k is a natural number so
let the sum of even integers to n=S
S=2(1+2+3+4+5+6+7+8+......+k-1+k
divide bith sides of equation 1 by 2
0.5S=1+2+3+4+5+...........+k-1+k
S=2(k+(k-1)+..............................+2+1)
divide both sides of equation 2 by 2
0.5S=k+k-1+..............................+2+1)
by adding both we will get
___________________________
S=(k+1)(k)
so the sum will be equal to
S=

so let us test the equation
for the first 3 even number there sums will be
2+4+6=12
by our equation 3^2+3=12
gave us the same answer so our equation is correct
Answer:

Step-by-step explanation:

Subtract 2 from both sides:


Subtract 5x from both sides:


Divide both sides by 2:

