In order to find how much money do pay each friend, you first stablish the situation in an algebraic way.
You have that one of them pay 1,5 times the payment of the otherone. Furthermore, the rent cost is 850. You can put it in the following form:
x + 1,5x = 850
where x is what one of the friend pays. You solve the previous equation for x, just as follow:
x + 1,5x = 850 you sum similar terms
2,5x = 850 you divide by 2,5
x = 850/2,5
x = 340
Then, one of the friend pays $340 and the other one pays 1,5(340) = $510
The sum of both payments must result $850, in fact:
$340 + $510 = $850