'budget-prioritized' originates from the combination of 'budget' and 'prioritize', where 'budget' refers to a financial plan and 'prioritize' means to arrange or deal with in order of importance.

'Budget' comes from the Old French word 'bougette', meaning 'small bag', and 'prioritize' is derived from 'priority', which comes from the Latin 'prioritas', meaning 'precedence'.

Initially, 'budget' referred to a physical bag for money, but over time it evolved to mean a financial plan. 'Prioritize' has maintained its meaning of arranging in order of importance.