An ion-exchange bed does not soften water a little. It takes hardness down to a fraction of a grain, and that is usually more softening than the building wants. The fix is plumbing, not chemistry: a bypass line carries some raw water around the vessel and rejoins the softened stream in the header. A smaller softener, less salt, and water at whatever hardness the specification asks for. Authored in grains per gallon and US gallons per minute, the units on the controller and the meters beside it.

$C = \dfrac{Q_1 C_1 + Q_2 C_2}{Q_1 + Q_2}$, read aloud C equals Q-one C-one plus Q-two C-two, all over Q-one plus Q-two. The subscript convention, stated once: subscript 1 is the raw-water bypass and subscript 2 is the softened stream. $Q_1$ and $Q_2$ are the two flows in gallons per minute. $C_1$ is the raw hardness and $C_2$ the hardness leaving the softener, both in grains per gallon. $C$, with no subscript, is the hardness of the blend after the streams join, and it is what you are solving for.

Read the top line as a rate. Gallons per minute times grains per gallon is grains per minute, the hardness each stream delivers. Hardness is neither made nor lost in the header, so the two rates add, and the total is carried by the combined flow underneath. The units are forgiving: any flow unit will do if both streams share it, and any hardness unit likewise, because each cancels against itself.

Two checks cost nothing. The blend must land between its two sources, because no mixture is ever stronger than its strongest stream or weaker than its weakest. And it is a weighted average, not a plain one: 20 gpm of raw water into 80 gpm of softened water lands far closer to the softened figure, because four fifths of the water came that way.

The design question runs backwards. Given the target, solve for the bypass flow: $Q_1 = Q_2\,\dfrac{C - C_2}{C_1 - C}$. It is a lever. Each flow is proportional to how far the target sits from the other stream, so a target close to the softened water needs only a little raw water. And when the blend and one source have been tested, the same balance recovers the other: $C_1 = \dfrac{C\,(Q_1 + Q_2) - Q_2 C_2}{Q_1}$.

One honest limit. The balance assumes nothing reacts when the streams meet. A softened water and its own raw supply blend cleanly. Two different waters may not, and pH never blends this way at all, because it is a logarithm.