Answer:
19 letters
Step-by-step explanation:
Suppose Number of Amy's full name letters = X
Number of Stephanie's full name letters = Y
Now, according to given condition that ''number of letters in Stephanie's full name is sixteen less than twice the number of letters in Amy's full name'',
Equation 1 becomes
Y = 2X-16
Now, according to second condition, product of their names' letter is 418. So,
Equation 2 becomes
XY = 418
Deducing value of X from equation 1,
X = (Y+16)/2
Putting this value in equation 2 we get,
{(Y+16)/2}*Y = 418,
By simplifying this equation we get a quadritic equation
(Y^2)+16Y-836=0
By breaking middle term (You can use quadratic formula here as well)
(Y^2)+38Y-22Y-836=0
Y(Y+38)-22(Y+38)=0
(Y-22)(Y+38)=0
At this stage we have two values for Y,
Y=22, or Y=-38
Now considering only positive value since the number of letters in a name can not be in negative number,
Y=22,
So X=(Y+16)/2
X=19
