SOLUTION: A salesman worked a certain numbers of days to earn $192. If he had been paid $8 more per day, he would have earned the same amount of money in 2 fewer days. How many days did he w

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Question 628555: A salesman worked a certain numbers of days to earn $192. If he had been paid $8 more per day, he would have earned the same amount of money in 2 fewer days. How many days did he work?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the actual number of days he worked
+192%2Fd+ = the actual amount of money he made each day
+192%2Fd+%2B+8+ = the amount of money he made each day plus $8
------------
given:
( daily earnings + $8 ) = ( daily earnings ) x ( 2 less days worked )
+192%2Fd+%2B+8+=++192+%2F+%28d-2%29++
Multiply both sides by +d%2A%28+d+-+2+%29+
+192%2A%28+d-2+%29+%2B+8%2Ad%2A%28+d-2+%29++=+192d+
+192d+-+384+%2B+8d%5E2+-+16d+=+192d+
+8d%5E2+-+16d+=+384+
+d%5E2+-+2d+=+48+
Complete the square
+d%5E2+-+2d+%2B+%28-2%2F2%29%5E2+=+48+%2B+%28-2%2F2%29%5E2+
+d%5E2+-+2d+%2B+1+=+49+
+%28+d+-+1+%29%5E2+=+7%5E2+
+d+-+1+=+7+
+d+=+8+
He worked 8 days
check:
+192%2Fd+%2B+8+=++192+%2F+%28d-2%29++
+192%2F8+%2B+8+=++192+%2F+%288-2%29++
+24+%2B+8+=+192%2F6+
+32+=+32+
OK