When you have an equation with more unknowns that constraints and you want to add some assumptions to solve it you may add a relative propensity calculation. Best served by an example.

Given:

 households[uss,usdt,th]
 population[uss,th]

Want to get:

 peoplePerHousehold[uss,usdt,th]

constraints:

 population[uss,th] = sum (households[uss,usdt,th] * peoplePerHousehold[uss,usdt,th]; dim=usdt)

makeup a relative propensity:

 relPopPersPerHH[usdt] = where each value is related to one of the entries 

Finally the math to calculate peoplePerHousehold[uss,usdt,th] is:

  !Equation A:
  local peoplePerHouseholdEst[uss,usdt,th] = households[uss,usdt,th] * peoplePerHousehold[usdt]
  !Equation B:
  peoplePerHousehold[uss,usdt,th] = population[uss,th] / peoplePerHouseholdEst[uss,usdt,th] * relPopPersPerHH[usdt]

You know your identity :

  population[uss,th] = households[uss,usdt,th] * peoplePerHousehold[uss,usdt,th]

substituting from your final math Equation B for personPerHousehold:

  population[uss,th] = households[uss,usdt,th] * population[uss,th] / peoplePerHouseholdEst[uss,usdt,th] * relPopPersPerHH[usdt]

reordering:

  population[uss,th] = households[uss,usdt,th] * relPopPersPerHH[usdt] * population[uss,th] / peoplePerHouseholdEst[uss,usdt,th]

Then notice the substitution can be done for Equation A from the final math above:

  population[uss,th] = peoplePerHouseholdEst[uss,usdt,th] * population[uss,th] / peoplePerHouseholdEst[uss,usdt,th]

And the estimates cancel so you have an identity and you are comfortable your math worked

  population[uss,th] = population[uss,th]