profit from two plots of land

Question

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

Answer 1

x + y = 120000

0.15x - 0.10y = 5500

 

Multiply both sides of bottom by 100 to remove decimals

 

x + y = 120000

15x - 10y = 550000

 

Multiply both sides of top by 10

 

10x + 10y = 1200000

15x - 10y = 550000

 

Add the two

 

25x = 1750000

x = 70000

He paid $70,000 for the property that made a profit, and paid $50,000 for the property that lost value.