Question

A state gets its money from a state lottery, a property tax, a sales tax of 5%, and an excise tax. This year it projects that it will receive $32 million from the state lottery, $40 million from the property tax, and $10 million from the excise tax. If the state needs $100 million to cover its expenses, how many dollars worth of taxable items must be purchased in the state this year for the state to break even?

Answer 1

for the state to break even, its expenses must equal its revenue

expenses = 100 million
income = 32 mill + 40 million + 10 million = 82 million + 0.05x

100,000,000 = 82,000,000 + 0.05x......with x being taxable income
100,000,000 - 82,000,000 = 0.05x
18,000,000 = 0.05x
18,000,000 / 0.05 = x
360,000,000 = x <===