Tim and George are the same height. Tim is 5/6 the height of their friend Peter, and George is 7/8 the height of Peter minus 2 and 1/4 inches. How tall Peter, Tim, and George?
Let P = height of Peter
Let T = height of Tim
Let G = height of George
T = G (Tim and George are the same height)
T = (5/6)P (Tim is 5/6 the height of their friend Peter)
G = (7/8)P - (2 1/4) (George is 7/8 the height of Peter minus 2 and 1/4 inches.)
Substituting for T = G in the 2nd 2 eqns,
G= (5/6)P
G = (7/8)P - (2 1/4)
Comparing the above two eqns,
(5/6)P = (7/8)P - (2 1/4)
(7/8)P - (5/6)P = 2 1/4 = 9/4
(21/24)P - (20/24)P = 9/4
P/24 = 9/4
P = 54
G = (7/8)P - (2 1/4) = (7/8)*54 - 9/4 = 189/4 - 9/4 = 180/4 = 45
G = 45
T = G = 45
The three boys heights are: Peter = 54, Tim = 45, George = 45