A flush tank on a toliet is rectangular with dimensions of 21 in. by 6.5 in. and contains water to a depth of 12 in. How many gallons of water per flush will be saved if the depth of water is reduced by one third? (231 in^3 per gallon.)

To find out how many gallons of water per flush will be saved, we need to calculate the volume of water in the flush tank both before and after reducing the depth by one third. Then, we can find the difference between these two volumes and convert it to gallons.

First, let's calculate the initial volume of water in the flush tank.

Volume of the flush tank = length × width × depth
Volume of the flush tank = 21 in × 6.5 in × 12 in

Next, let's calculate the new volume of water after reducing the depth by one third.

Reduced depth = depth - (1/3) × depth
Reduced depth = 12 in - (1/3) × 12 in

New volume of water in the flush tank = length × width × reduced depth
New volume of water in the flush tank = 21 in × 6.5 in × reduced depth

Finally, let's find the difference between the initial volume and the new volume and convert it to gallons.

Volume saved per flush = (Volume of the flush tank - New volume of water in the flush tank) / 231 in^3 per gallon

Now, we can substitute the values and calculate the answer.

Initial volume of water in the flush tank = 21 in × 6.5 in × 12 in
New volume of water in the flush tank = 21 in × 6.5 in × reduced depth
Reduced depth = 12 in - (1/3) × 12 in

After calculating these values, you can find the volume saved per flush by subtracting the new volume from the initial volume, and then divide that by 231 to convert the volume to gallons.

Remember to use consistent units throughout the calculations.