A woman invested part of $21,500 at 5% interest and the rest at 7%. If her annual interest is $1,215, how much did she invest at 5%?

Question

Yes, I need help with solving this college algebra math problem.

Answer 1

Hello, thank you for taking the time to post your question!

The key on solving this type of question is to set up an algebraic expression that represents the underlying data. On this one we have

x + y = 21500   since the investments have to sum to be $21,500 in total

0.05x + 0.07y = 1215   since she earns 5% interest and 7% interest to get $1,215 in interest

I would substitute in the first equation into the second and then solve algebraically! when I do that I get

x = 14500, meaning that y = 21500 – 14500 = 7000

so she invested $14,500 at the 5% interest rate

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

x=amount invested at 5%

1215=5%x+7%(21,500-x)

1215=0.05x+0.07(21,500-x)

1215=0.05x+1505-0.07x

1215=1505-0.02x

1215-1505=-0.02x

-290=-0.02x

290=0.02x

29,000=2x

x=29,000/2

x=$14,500 invested at 5%