Find count(s) from percentage(s)

multi.py

import numpy as np

goal_fracs = np.array([.1, .9])
goal_fracs = np.array([.04, .04, .11, .14, .67])
counts = np.zeros_like(goal_fracs)
n = 1
tol = .001

a = 0

while True:
    
    fracs = counts / n
    if np.allclose(fracs, goal_fracs, atol=tol):
        break
        
    if sum(fracs) < 1:
        i = np.argmin(fracs - goal_fracs)
        counts[i] += 1
    else:
        n += 1
    
counts, n

single.py

goal_frac = .2
k = 0
n = 1
tol = .01

while True:
    
    frac = k / n
    if math.isclose(frac, goal_frac, abs_tol=tol):
        break
    
    if frac < goal_frac:
        k += 1
    else:
        n += 1
    
k, n