Finding 'x' in Excel

Question

I have a problem I need help with, please.

I want to find x in the following manner:

((a+x)/(b+x))>=c

This would be an extension to a simple calculation in my workplace, d=a/b where:

• b is the total number of incoming calls we receive
• a is the number of calls we could handle out of b, the total
• d shows our performance

So far so good. No function needed.

But we also have a target, c, in percentage - let's say 60% or 0.6 Ideally a/b should be bigger than c.

IF it is not, I'd like to know how many more incoming calls we need that are also handled (with x added to both a and b above) therefore slowly raising our performance over time.

x would show this extra number of handled calls, say, "5"

• I do not know what type of mathematics it is (I cannot recall it, shame on me)
• I do not know how to achieve it in Excel

Can someone please help? thank you!

Answer 1

This might be a case for a graphical presentation:

where the formula in F2 (copied down) is =IF(E2>0,E2,0) and a Stacked Column has been applied.

Answer 2

When you cannot solve the equation "analytically", you might use the "goal seek".

Use a param in any range, such as "A1". Fill it with any value looking like your answer (if you want a percentage put 50%, etc.).

A1=3
B1=((a+A1)/(b+A1))

Open "Data" tab and "What-If analysis" and "Goal Seek".

In "Set Cell", select "B1" In "To Value", set the value you want to reach (0.6 in your sample) In "By changing cell", set A1.

Click OK, see A1 becoming the expected result.

Answer 3

((a+x)/(b+x))>=c

then

a+x >= c(b+x)

then

a+x >= cb+cx

then

a-cb >= cx-x

then

a-cb >= (c-1)x

then

(a-cb)/(c-1) >= x

So if you have values for a,b,c then the range for x is defined.