Question 244436: At a gathering of professionals, all but 30 were musicians; all but 40 were pediatricians; and all but 50 were journalists. Each person has exactly one profession. If only musicians, journalists, and pediatricians attend this gathering, how many journalists were present?
A. 10 B. 20 C. 30 D. 60 E. 70
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! all but 30 were musicians
all but 40 were pediatricians
all but 50 were journalists.
let m = number of musicians
let p = number of pediatricians
let j = number of journalists
let s = m + p + j
m = s - 30
p = s - 40
j = s - 50
s = m + p + j
substitute for m and p and j to get:
s = s - 30 + s - 40 + s - 50
combine like terms to get:
s = 3s - 120
add 120 to both sides of equation and subtract s from both sides of equation to get:
2s = 120
solve for s to get:
s = 60
since s = 60, then substitute 60 for s in the following equations to get:
60 = m - 30
m = 30
60 = p - 40
p = 20
60 = j - 50
j = 10
you have:
30 musicians
20 pediatricians
10 journalist
total is equal to 60
all but 30 are musicians means that 60 - 30 = 30 musicians
all but 40 are pediatricians means that 60 - 40 = 20 pediatricians
all but 50 are journalists means that 10 are journalists
your answer is that the number of journalists is equal to 10.
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