4. A group of four friends want to pay a joint bill of 56 kuna at a café. Checking how much money each of them has, they discovered that without Josip's money they have 85 kuna, without Mark's money 90 kuna, without Franja's money 88 kuna, and without Luka's money 94 kuna. Which pair of friends together have exactly the amount of money that the bill costs?
4. Let's denote the amount of money Josip has as J, Marko's as M, Franjo's as F, and Luka's as L.

It is given that:

$\mathrm{M}+\mathrm{F}+\mathrm{L}=85 \mathrm{kn}$

$\mathrm{J}+\mathrm{F}+\mathrm{L}=90 \mathrm{kn}$

$\mathrm{J}+\mathrm{M}+\mathrm{L}=88 \mathrm{kn}$

$\mathrm{J}+\mathrm{M}+\mathrm{F}=94 \mathrm{kn}$

2 POINTS

By adding all the equations, we get:

$3 \cdot(\mathrm{J}+\mathrm{M}+\mathrm{F}+\mathrm{L})=357 \mathrm{kn}$, or 2 POINTS

$\mathrm{J}+\mathrm{M}+\mathrm{F}+\mathrm{L}=119 \mathrm{kn}$ 1 POINT

Now it is easy to calculate that Josip has $119-85=34 \mathrm{kn}, \quad 1$ POINT

Marko has $119-90=29 \mathrm{kn}, \quad 1$ POINT

Franjo has $119-88=31 \mathrm{kn} \quad 1$ POINT

and Luka has $119-94=25$ kn. 1 POINT

The correct amount to pay the bill is with Franjo and Luka. 1 POINT

TOTAL 10 POINTS