Problem: Four boys bought a boat for $60. The first boy paid one half of the sum of the amounts paid by the other boys; the second boy paid one third of the sum of the amounts paid by the other boys; and the third boy paid one fourth of the sum of the amounts paid by the other boys. How much did the fourth boy pay?
Answer Choices:
A. $10
B. $12
C. $13
D. $14
E. $15
Solution:
Let w,x,y and z be the amounts paid by the first, second, third and fourth boy, respectively Then since
w+x+y+z=60w=21(x+y+z)=21(60−w),w=20x=31(w+y+z)=31(60−x),x=15y=41(w+x+z)=41(60−y),y=12 and z=13.