[High School- Algebra 2] System of Equations (Word Problems)

[powerfull]

Well, in class, we were given this extra credit packet to work on over the break (Tuesday - Sunday). I'm stuck on one problem (for now) and was wondering if someone could give me some guidance on how to solve it (Because the rest of the packet is similar).

Directions: Use Systems of Equations to solve.

- Sarah borrowed $6,000, part at 15.5% and the rest at 14.25%. At the end of 3 years and 6 months, he had paid $3,150 in simple interest. How much did he borrow at each rate?

(Yes, in the question, it does say "he".) I got an answer, but I don't think it's right:



Sorry for the somewhat sloppy work. If you have any questions about the question or my work just ask. Thanks for any help or tips.

[tangomango]

Ahh, I think I see your mistake. You need the move the decimal place over when converting % to decimal. Change 15.5% to .155 and 14.25% to .1425 and do what you did.

[powerfull]

Oh thanks. My friend just informed me about that a few minutes ago. I'll try it again.

[tangomango]

I hate making stupid mistakes too >_>

In the future, if you get a negative number for an answer in a word problem, it usually means that you did something wrong in your steps. Unless you are doing something that has more than one answer.

Also, I don't know what you got for the answer, but when I did part of the equation, it had long decimals.

[powerfull]

Yeah, that's why I thought it was wrong, because I had a negative number. After I try it again, should I post my new answer?

[Silvuh]

As mentioned, the percents weren't properly converted in to decimals. But, they shouldn't be in the first equation. If you borrow 6000 dollars and split it between rates, well. The equation should simply be a split: X + Y = 6000. No rates involved.

And your equation 3.5(X+Y) = 3150 is saying that the rates are both 100%. Or, I = Pt. (Also, if you divide out the 3.5, you get X+Y=900, which means that you only have 900 dollars to start out with, and that's not true.)
The formula for simple interest is I = Prt. This is where you put the rates in.
The second equation should be 3.5 ( 0.155X + 0.1425Y ) = 3150.

Basically, you put your rates in the wrong equation.

And you can solve it from here.

At least I think this is right...

[tangomango]

Originally Posted by Silvuh

As mentioned, the percents weren't properly converted in to decimals. But, they shouldn't be in the first equation. If you borrow 6000 dollars and split it between rates, well. The equation should simply be a split: X + Y = 6000. No rates involved.

Wow, how did I miss that lol.

[powerfull]

Thanks you two.
My final answer was Sarah saved $5932.35 at 15.5% and he saved $67.65 at 14.25%. Hope it's right.