Let the amount of money that is divided be C.

It is divided in the ratio 10 : 7 : 5 among X, Y, Z.

This can be written in another way as X gets 10/ 22 of the amount, Y gets 7/22 of the amount and Z gets 5/22 of the amount.

As Y gets $14 more than Z

(7/22)*C - (5/22)*C = 14

=> C*( 2/ 22) = 14

=> C = 14*11

=> C = 154

The amount that X gets is (10/ 22)*154 = 70

The required value for the total amount is $154 and X gets $70.