Table 3.

Algebraic manipulation of previous equations.

We know that	We know that
z = x * se + y * (1-sp)	z = x * se + y * (1-sp)
y = p * x	x = y / p
which means that	which means that
z = x * se + p * x * (1 - sp)	z = (y / p) * se + y * (1 - sp)
we solve for x	we solve for y
x = z / (-sp * p + se + p)	y = p * z / (-sp * p + se + p)
For the previous example with z = 100 000 and p= 2.5 we get
x =	215 054
y =	537 634
I have again written a udf in VBA
Lyme2(se ; sp ; p ; z ; output) where output is either "x", "y" or "zz"
Lyme2(0.44;0.99;2.5;100000;"x")	x =	215 054
Lyme2(0.44;0.99;2.5;100000;"y")	y =	537 634
Lyme2(0.44;0.99;2.5;100000;"zz")	zz =	13.29
we know that	we know that
zz = (z / (x + y)) * 100	zz = (z / (x + y)) * 100
y = p * x	x = y / p
which means that	which means that
zz = (z / (x + p * x)) * 100	zz = (z / ((y / p) + y)) * 100
we solve for x	we solve for y
x = 100 * z / (p * zz + zz)	y = 100 * p * z / (p * zz + zz)
For the previous example with z=100 000, zz =13.29 and p= 2.5 we get
x =	215 054
y =	537 634
I have again written a udf in VBA
Lyme3(se ; sp ; p ; z ; zz ; output) where output is either "x", "y"
Lyme3(0.44;0.99;2.5;100000;13.29;"x")	x =	215 054
Lyme3(0.44;0.99;2.5;100000;13.29;"y")	y =	537 634