Half a ride

Three friends shared a taxi home. The whole ride cost sixty tokens, and the first friend got out halfway.

The fare is $60$ tokens; the first friend got out halfway.

Fare $F=60$; halves $\frac{F}{2}=30$.

One of them said: twenty each! But that was not fair: the first friend had only ridden half the way.

An equal split, $\frac{60}{3}=20$ each, is not fair.

Equal split $\frac{60}{3}=20$: not fair.

The first half of the ride, thirty tokens, was ridden by all three, so ten tokens each. The second half, another thirty tokens, was ridden by two, so fifteen each.

The first half costs $\frac{60}{2}=30$, shared by $3$: $\frac{30}{3}=10$ each. The second half costs $30$, shared by $2$: $\frac{30}{2}=15$ each.

Per person: $a=\frac{30}{3}=10$ in the first half and $b=\frac{30}{2}=15$ in the second.

So the first friend pays ten, and the other two pay ten plus fifteen, that is twenty-five each. Ten and twenty-five and twenty-five make sixty. The two who stayed paid more than twenty, and all three agreed it was fair.

The first pays $10$; the other two pay $10+15=25$ each, and $10+25+25=60$.

$x_1=a=10$ and $x_2=x_3=a+b=25$, with $x_1+x_2+x_3=60✓$