Four students at a computer fair competed against each other in a space-travel game. Chris scored 2/3 as many points as the winner Pat. Rich scored 1/2 as many points as Chris. Tome scored 100 points, which was 90 points less than Rich's score. How many points did Pat score?

Answer 1

what do we know?

c = 2/3 p
r = 1/2 c
t = 100 = r-90

So, what is p?

p = 3/2 c
= 3/2 (2r) = 3r
= 3(t+90)
= 3(190)
= 570

Answer 2

Pat - x
Chris - 2/3x
Rich - 1/2*2/3x = 1/3x
Tom - 1/3x - 90 = 100

1/3x = 190
x = 570