SOLUTION: Bob Brown bought two plots of land for a total of $110,000. On the first plot, he made a profit of 16%. On the second, he lost 4%. His total profit was $9600. How much did he pay

Algebra ->  Proportions  -> Lessons -> SOLUTION: Bob Brown bought two plots of land for a total of $110,000. On the first plot, he made a profit of 16%. On the second, he lost 4%. His total profit was $9600. How much did he pay       Log On


   



Question 499028: Bob Brown bought two plots of land for a total of $110,000. On the first plot, he made a profit of 16%. On the second, he lost 4%. His total profit was $9600.
How much did he pay for each piece of land.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = amount he paid for 1st plot
Let b = amount he paid for 2nd plot
given:
(1) +a+%2B+b+=+110000+
(2) +.16a+-+.04b+=+9600+
---------------------
(2) +16a+-+4b+=+960000+
Multiply both sides of (1) by 4
and add (1) and (2)
(1) +4a+%2B+4b+=+440000+
(2) +16a+-+4b+=+960000+
+20a+=+1400000+
+a+=+70000+
and, since
(1) +a+%2B+b+=+110000+
(1) +70000+%2B+b+=+110000+
(1) +b+=+40000+
She paid $70,000 for the 1st plot
and $40,000 for the 2nd plot
check the answer:
(2) +.16a+-+.04b+=+9600+
(2) +.16%2A70000+-+.04%2A40000+=+9600+
(2) +11200+-+1600+=+9600+
(2) +9600+=+9600+
OK