How many gallons can a 50,000 grain softener soften with 45 grain water before it requires regeneration?

To determine how many gallons a 50,000 grain softener can soften before regeneration is required, you can use a simple calculation based on the capacity of the softener and the hardness of the water.

The capacity of the softener is 50,000 grains. The water hardness is given as 45 grains per gallon. To find the total number of gallons that can be softened, you divide the total capacity of the softener by the hardness level of the water:

[

\text{Gallons softened} = \frac{\text{Capacity of the softener}}{\text{Hardness of water}}

]

Plugging in the numbers:

[

\text{Gallons softened} = \frac{50,000 \text{ grains}}{45 \text{ grains/gallon}}

]

This calculation results in approximately 1,111.11 gallons. Since you can only deal in whole gallons, the softener will effectively manage about 1,100 gallons of water before regeneration is needed.

This understanding of calculating softener capacity includes knowing how to apply the grain capacity to water hardness, making option 1,100 gallons the correct choice. The other options either overestimate or underestimate the actual capacity of