Problem: A dealer bought n radios for d dollars, d , a positive integer. He contributed two radios to a community bazaar at half their cost. The rest he sold at a profit of $8 on each radio sold. If the overall profit was $72, then the least possible value of n for the given information is:
Answer Choices:
A. 18
B. 16
C. 15
D. 12
E. 11
Solution:
(n−2)(nd+8)+2⋅2nd=72+d,8n2−88n−d=0,n2−11n−8d=0. Since n is a (least positive) integer, d must be such that n2−11n−8d yields linear factors with integer coefficients. Hence d=96 and 8d=12 so that n2−11n−12=(n−12)(n+1)=0 and n (least) =12.
or
Since 8n2−88n−d=0,88=8n−nd whence n can be any integer >11.