Problem Solving

Can you please help in explaining the solution to this problem

Ms. Adams sold two properties, X and Y, for $30,000 each. She sold property X for 20% more than she paid for it and sold property Y for 20% less than she paid for it. If expenses are disregarded, what was her total net gain or loss, if any, on the two properties?

A. Loss of $1,250
B. Loss of $2,500
C. Gain of $1,250
D. Gain of $2,500
E. There was neither a net gain nor a net loss

thanks

The selling price of property X is 20% more than what she paid for it, meaning that 30 000 = 120%*(price paid for X), making the price paid for X 30 000/1.2 = 25 000.
The selling price of property Y is 20% less than what she paid for it or 30 000 = 80%*(price paid for Y), making the price paid for Y 30 0000/0.8 = 37 500.
This means that she gained 5 000 from selling X, but she lost 7 500 from selling Y. At the end of the day, she lost 2 500.

DanaJ

Please if you could explain step by step it will be very much appreciated

thanks

I don't think you can break it down more than Dana did, but I'll try. . .The underlying concept here is percent change.

The problem give us the selling price, so we need to find the original price of each property before their respective increase and decrease in price.

Step 1-The selling price of the first property is $30,000. this is the price AFTER an increase of 20%, so the original price is x times 1.20 since the price INCREASED 20%. That leaves us with x*1.20=30,000------->x=25,000. Thus, the price increased $5,000

Step 2-The selling price of the Property y is 30,000. This is the price AFTER a decrease of 20%, so the original price is y times .80 since 1.00-.20=.80. That leaves us with y*.80=30,000-------y=37,500. Thus the price decreased 75,00

Finally, we need to find out whether or not Ms. Adams made money. So we vet the two prices. 5000-7500=-2500. So overall,
she lost 2500.

This problem is a lot easier to manage if you make a table using the formula for percent change.