Write an equation that models the described quantity. Specify what each variable

Question

Write an equation that models the described quantity. Specify what each variable represents. A tub contains 20 gallons of water and is being filled at a rate of 3 gallons per minute. A pool contains 12,000 gallons of water and is being drained at a rate of 9 gallons per minute. The circus charges $12 for adult admission and $8 for a child. There were 1, 280 people at the circus. The admission receipts were $11, 840. How many adults and how many children attended? There were 1200 people at a pool. The admission receipts were $9, 600. The admission price was $10 for adults and $4 for children. How many adults and how many children attended?

Explanation / Answer

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Given

Initial Volume (V0)= 20 gallons

Rate of Change of Volume (dV/dt) = 3 gallons /min

                                                        = 3*60 = 180 gallons / hr

Volume at any time t (in hr) is given by

V(t) = V0 + dV/dt

Integrating from 0 to t

V(t) = 20 + 180t   Solution

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