SOLUTION: Stuart agrees to a house - painting job for 900$. he takes 4 days longer than expected, and he has earned 18.75$ less per day than expected. in how many days did he expect to compl

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Stuart agrees to a house - painting job for 900$. he takes 4 days longer than expected, and he has earned 18.75$ less per day than expected. in how many days did he expect to compl      Log On


   



Question 271324: Stuart agrees to a house - painting job for 900$. he takes 4 days longer than expected, and he has earned 18.75$ less per day than expected. in how many days did he expect to complete the house?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let d = number of days he expected job to take
given:
d+%2B+4 = number of days job actually took
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900%2F%28d+%2B+4%29+=+900%2Fd+-+18.75
Multiply both sides by d%2A%28d+%2B+4%29
900d+=+900%2A%28d+%2B+4%29+-+18.75%2Ad%2A%28d+%2B+4%29
900d+=+900d+%2B+3600+-+18.75d%5E2+-+75d
18.75d%5E2+%2B+75d+-+3600+=+0
I'll solve with quadratic formula
d+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+18.75
b+=+75
c+=+-3600
d+=+%28-75+%2B-+sqrt%28+75%5E2-4%2A18.75%2A%28-3600%29+%29%29%2F%282%2A18.75%29+
d+=+%28-75+%2B-+sqrt%285625+%2B+270000+%29%29%2F37.5+
d+=+%28-75+%2B-+sqrt%28275625%29%29%2F37.5+
d+=+%28-75+%2B-+525%29%2F37.5+
d+=+%28-75+%2B+525%29%2F37.5
d+=+12
He expected to complete the house in 12 days
check:
900%2F%28d+%2B+4%29+=+900%2Fd+-+18.75
900%2F%2812+%2B+4%29+=+900%2F12+-+18.75
multiply both sides by 12%2A16
900%2A12+=+900%2A16+-+18.75%2A12%2A16
10800+=+14400+-+3600
10800+=+10800
OK