Ranch home is 2100 sq ft (70 x 30)

Assume the climate yields 30in of rainfall per year.
Baths, showers, faucets use 40% of this water, of which 80% is recycled to the indoor garden (50 ft x 20 ft)

How much water in INCHES will the 50ft x 20 ft indoor garden receive per year from the recycled water?

I've tried
2100 x 2.5ft rain = 5280 cu ft
5280 cu ft x .40 x .80 = 1680 cu ft

am I on the right track?
where do I go from here?

50*20 = 1000 square feet

so we use 1680/1000 = 1.680 ft on pool
1.680 * 12 = 20.16 inches used

but there is an easier way

30 in * (2100/1000) * .4*.8
= 20.16 in

Yes, you are on the right track! Let's break down the calculation further to find the amount of water the indoor garden will receive per year:

First, convert the square footage of the indoor garden into square inches:
50 ft x 20 ft = 1000 square feet
1000 square feet x 144 square inches/square foot = 144,000 square inches

Next, calculate the volume of water that 40% of the total rainfall corresponds to:
5280 cubic feet x 0.40 = 2112 cubic feet

Now, convert the volume of water to cubic inches:
1 cubic foot = 12 inches x 12 inches x 12 inches = 1728 cubic inches
2112 cubic feet x 1728 cubic inches/cubic foot = 3,652,416 cubic inches

Since 80% of this water is recycled to the indoor garden, calculate the amount of water the garden will receive:
3,652,416 cubic inches x 0.80 = 2,921,932.8 cubic inches

Finally, convert the volume to inches:
2,921,932.8 cubic inches / 144,000 square inches = 20.29 inches

Therefore, the 50 ft x 20 ft indoor garden will receive approximately 20.29 inches of water per year from the recycled water.

Remember to double-check the calculations to ensure accuracy.