How do I get budgeted activity level?

Hi, sir. I have a problem with following question,

The pharmacy in a busy hospital uses pre-determined rates for absorbing total overheads, based on the budgeted number of prescriptions to be handled. A rate of $7 per prescription has been calculated, and the following overhead expenditures have been estimated at two activity levels.

Total overheades
$97,000
Number of prescriptions
13,000
—————————————–
Total overheades
$109,000
Number of prescriptions
16,000

During a particular period fixed overheads were $45,000.

Based on the data above, what was the budgeted level of activity in prescriptions to be handled during the period in question?

(a) 13,000
(b) 15,000
(c) 16,000
(d) 33,333

And, I have searched for the answer then it said 15,000 is correct. I also looked at explanation which was-

Variable OH + Fixed OH = Total OH OH
[Fixed OH per prescription = $7 – $4 = $3]
Total Fixed OHs = $45,000

>> Budgeted Activity Level <<
$45,000/$3 = 15,000 prescriptions

But the part I don’t understand is where the value of $4 comes from.

Sir, would you please explain furthermore with details?

Thank you.