SOLUTION: tom mowed lawns a certain number of days to earn $300. if he had received $3 less per day, he would have had to work 5 days longer to earn the same amount. how many days did he wor

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: tom mowed lawns a certain number of days to earn $300. if he had received $3 less per day, he would have had to work 5 days longer to earn the same amount. how many days did he wor      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 460607: tom mowed lawns a certain number of days to earn $300. if he had received $3 less per day, he would have had to work 5 days longer to earn the same amount. how many days did he work.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let d = number of days he worked
Let a = amount he earned per day
given:
(1) +300+=+d%2Aa+
(2) +300+=+%28+d%2B5+%29%2A%28+a+-+3+%29+
---------------------
(2) +300+=+d%2Aa+%2B+5a+-+3d+-+15+
(2) +300+=+300+%2B+5a+-+3d+-+15+
(2) +5a+-+3d+=+15+
and, from (1),
(1) +a+=+300%2Fd+
so,
(2) +1500%2Fd+-+3d+=+15+
(2) +1500+-+3d%5E2+=+15d+
(2) +3d%5E2+%2B+15d+-+1500+=+0+
(2) +d%5E2+%2B+5d+-+500+=+0+
+d+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+1+
+b+=+5+
+c+=+-500+
d+=+%28-5+%2B-+sqrt%28+5%5E2-4%2A1%2A%28-500%29+%29%29%2F%282%2A1%29+
d+=+%28-5+%2B-+sqrt%28+25+%2B++2000+%29%29+%2F+2+
+d+=+%28+-5+%2B+sqrt%282025%29%29+%2F+2+
+d+=+%28+-5+%2B+45+%29+%2F+2+
+d+=+20+ ( note: can't use the (-) sqrt )
He worked 20 days
check:
(1) +300+=+d%2Aa+
(1) +300+=+20a+
(1) +a+=+15+
(2) +300+=+%28+20%2B5+%29%2A%28+15+-+3+%29+
(2) +300+=+25%2A12+
(2) +300+=+300+
OK