Roger bought two plots of land for a total of $120,000. sold the first plot, he made a profit of 15%. sold the second. he lost 10%. total profit was $5500. How much did he pay for each piece of land?

Question

This is a question on a homework assignment that I can't figure out. I'm not sure how to set up the equation

Answer 1

Let "f" be the amount he paid for the first plot and "s" be the amount he pair for the second plot.

Then, since the total paid was $120,000:

f + s = 120000 or f = 120000 - s

A 15% profit means the profit would be 0.15f and a 10% loss means -0.10s so:

0.15f - 0.010s = 5500

Since "f" is the same as "120000 - s" then we can plug "120000 - s" into the second equation in place of "f":

0.15(120000 - s) - 0.10s = 5500

18000 - 0.15s - 0.10s = 5500

-0.25s = -12500

s = -12500/-0.25 = 50000

Since he paid $50,000 for the second plot, then he must have paid 120,000 - 50,000 or $70,000 for the first plot.

: