Question

One month Ruby worked 6 hours more than Isaac, and Svetlana worked 4 times as many hours as Ruby. Together they worked 126 hours. Find the number of hours each person worked.

Answer 1

let number of hours of Isaac,Ruby and Svetlana worked be x,y and z respectively. so y= x+6 ( equation 1) note: Ruby (y) worked 6 hours more than Isaac (x) z = 4 x y ( equation 2) note : Svetlana (z) worked 4 times as many hours as Ruby (y) x+y+z= 126 ( equation 3) note: Together they (x,y,z) worked 126 hours. substitute eqn 1 to eqn 3 so x+y+z= 126 becomes y-6 + y+z-126 2y+z= 126+6 2y+z=132 (equation 4) the substitute eqn 2 in eqn 4 so 2y+z=132 becomes 2y+4y=132 6y=132 y=132/6= 22 so y=22 substitute y value in equation 1 so y= x+6 becomes x+6=22 and x= 22-6 = 16 and substitute x and y values in equation 3 so 16+22+z= 126 38+z= 126 z= 126 -38 = 88 So the number of hours Isaac worked (x) is 16 hours number of hours Ruby worked (y) is 22 hours number of hours Svetlana worked (z) is 88 hours