SOLUTION: A reservation clerk worked 14.4 hours one day. She spent twice as much time entering new reservations as she did verifying old ones and one and a half as much time calling to confi

Algebra ->  Equations -> SOLUTION: A reservation clerk worked 14.4 hours one day. She spent twice as much time entering new reservations as she did verifying old ones and one and a half as much time calling to confi      Log On


   

Question 359159: A reservation clerk worked 14.4 hours one day. She spent twice as much time entering new reservations as she did verifying old ones and one and a half as much time calling to confirm reservations as verifying old ones. How much time did she spend entering new reservations
Answer by aggie_tutor(13) About Me  (Show Source):
You can put this solution on YOUR website!
total hours worked: 14.4
time on entering new = n
time on verifying old = p
time on confirming = r
n + p + r = 14.4
2p+=+n+ (two times the old)
1%281%2F2%29p+=+r (one and a half times the old)
substitute for r and n:
2p+%2B+p+%2B+1%281%2F2%29p+=+14.4
solve for p:
2p+%2B+1p+%2B+%283%2F2%29p+=+14.4
3p+%2B+%283%2F2%29p+=+14.4
to add the fraction to the 3p, you must convert 3p to common denominator:
%283%2F1%29+x+%282%2F2%29+=+%286%2F2%29
%286%2F2%29p+%2B+%283%2F2%29p+=+14.14
combine the like terms with the numerators on top:
%28%286+%2B+3%29%2F%282%29%29p+=+14.4
%289%2F2%29p+=+14.4
remove denominator by multiplying both sides by 2:
%282%29%289%2F2%29p+=+14.4%282%29
9p+=+28.8
p+=+28.8+%2F+9
p+=+3.2+hours
Now solve for
2p+=+n
2%283.2%29+=+n
6.4+=+n
Time spent on new reservations = n = 6.4 hours.
Double check your work by finding the r value, time spend confirming:
1%281%2F2%29p+=+r
1.5p+=+r
1.5%2A3.2+=+4.8+=+r+
Time spent on calling to confirm = r = 4.8 hours.
total time should = 14.4 hours:
r + n + p = 14.4
4.8 + 6.4 + 3.2 = 14.4