the lever rule

Picture the tie line as a see-saw, with your overall composition sitting at the pivot. The two phases sit at the two ends. Just like a see-saw, the phase that sits farther from the pivot must be present in the smaller amount, and the length of the arm on the opposite side gives each phase's weight fraction. It literally balances the amounts of the two phases.

More precisely, on a tie line the fraction of a phase equals the length of the opposite arm divided by the total tie-line length. Worked example: an alloy at 40% B, on a tie line running from an alpha phase at 20% B to a beta phase at 60% B. The fraction of the 60%-phase is (40 - 20)/(60 - 20) = 20/40 = 0.5, and the fraction of the 20%-phase is (60 - 40)/(60 - 20) = 0.5. So the mix is 50-50. In symbols, W_alpha = (C_beta - C0)/(C_beta - C_alpha), always using the arm on the far side of the overall composition C0.

This is how you turn a phase diagram into real numbers: how many kilograms of liquid versus solid in a casting, or how much pearlite versus proeutectoid ferrite in a steel. The opposite-arm rule trips people up: the phase whose composition lies nearest to your overall composition is the more abundant one. Amounts come out as weight fractions unless the diagram axis is in atomic percent.