Problem:
If a+1=b+2=c+3=d+4=a+b+c+d+5, then a+b+c+d is
Answer Choices:
A. −5
B. −10/3
C. −7/3
D. 5/3
E. 5
Solution:
From the given information,
(a+1)+(b+2)+(c+3)+(d+4)=4(a+b+c+d+5),
so
(a+b+c+d)+10=4(a+b+c+d)+20
and a+b+c+d=−310.
Note that a=d+3,b=d+2, and c=d+1. So,
a+b+c+d=(d+3)+(d+2)+(d+1)+d=4d+6.
Thus, d+4=(4d+6)+5, so d=−7/3, and
a+b+c+d=4d+6=4(−37)+6=−310.
Answer: B.
The problems on this page are the property of the MAA's American Mathematics Competitions