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PSAT/NMSQT
PSAT Math Test - No Calculator Section

Population vs. Housing Units Inequality

Hard Heart Of Algebra Linear Equations And Inequalities

In a small town, the population is modeled by the equation $$p(t) = 15000 + 500t$$, where $$p$$ is the population in the year $$t$$, and $$t$$ is the number of years since 2020. Simultaneously, the number of available housing units is represented by $$h(t) = 12000 + 250t$$, where $$h$$ is the number of housing units available in the same year.

To avoid overcrowding, the town aims to maintain at least 10% more housing units than the population. Determine the year when the number of housing units will first become less than 10% above the population. Provide your answer as a whole number.

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