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.

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

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