The number of letters in Stephanie's full name is sixteen less than twice the number of letters in Amy's full name. If the number of letters in Stephanie's full name is multiplied by the number of letters in Amy's full name and the product is 418, then how many letters are in Amy's full name?

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