Brine Tank

A 700 gallon tank has 600 gallons of salt water in it; the amount of salt dissolved in the water is a half-pound per gallon. An intake valve is opened and another 100 gallons of brine is allowed to flow into the tank; this brine has 2 pounds of salt per gallon. The tank is now full. Its contents are thoroughly stirred, and then an outlet valve is opened and 100 gallons of the mixture are drained out. This process is repeated two more times. At the end, how much salt per gallon is in the 600 gallons that remain in the tank?


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At the beginning: 300 lb. of salt in the tank.

Addition #1: 200 lb. → total = 500 lb. (5/7 lb./gal.)

Drain #1: 500 lb – 500/7 lb = 3000/7 lb. in 600 gal.

Add #2: 3000/7 + 200 = 4400/7 lb. of salt in 700 gal: 44/49 lb./gal.

Drain #2: 4400/7 – 4400/49 = 26400/49 lb. in 600 gal.

Add #3: 26400/49 + 200 = 36200/49 lb. of salt in 700 gal: 362/343 lb/gal.

Drain #3: 36200/49 – 36200/343 = 217,200/343 in 600 gal. or 1.055 lb./gal.

The concentration of salt doesn’t change after drain #3: 362/343 = 1.055 lb/gal.

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