A residential building contractor borrowed $39,000 to complete a new home. Some of the money was borrowed at 5%, some at 4%, and some at 6%. How much was borrowed at each rate if the annual interest owed was $1800 and the amount borrowed at 4% is four times more than the amount borrowed at 6%?

A. $12,000 at 5%; $22,000 at 4%; $5000 at 6%
B. $14,000 at 5%; $20,000 at 4%; $5000 at 6%
C. $12,000 at 5%; $21,000 at 4%; $6000 at 6%
D. $13,000 at 5%; $18,000 at 4%; $7000 at 6%
E. $11,000 at 5%; $24,000 at 4%; $6000 at 6%

Question

A residential building contractor borrowed $39,000 to complete a new home. Some of the money was borrowed at 5%, some at 4%, and some at 6%. How much was borrowed at each rate if the annual interest owed was $1800 and the amount borrowed at 4% is four times more than the amount borrowed at 6%?

A. $12,000 at 5%; $22,000 at 4%; $5000 at 6%	
B. $14,000 at 5%; $20,000 at 4%; $5000 at 6%
C. $12,000 at 5%; $21,000 at 4%; $6000 at 6%	
D. $13,000 at 5%; $18,000 at 4%; $7000 at 6%
E. $11,000 at 5%; $24,000 at 4%; $6000 at 6%

anonymous · Answer

Any ideas on how you want to attempt this problem? There are many many ways.

anonymous · Answer

Whatever way is easiest....

anonymous · Answer

I figured setting up a formula and then plugging in the different answers till I find the right one.. so in that case I guess I'm not sure what my equation/formula would be?

anonymous · Answer

Ok, well let's look at this.

anonymous · Answer

The easiest method by far in multiple choice questions is elimination.

anonymous · Answer

Four percent of $39,000 is?

anonymous · Answer

$1560

anonymous · Answer

Oh sorry, I didn't not read the question carefully enough.

anonymous · Answer

Let's do some elimination: can you tell me which letters do not fit this qualifier?  "
the amount borrowed at 4% is four times more than the amount borrowed at 6%"

anonymous · Answer

uhm... I'm not sure I understand your question....

anonymous · Answer

Oh, no problem.

Let's look at this:
$12,000 at 5%; $22,000 at 4%; $5000 at 6%

For this answer, is the 4% value 4x the amount of the 6% value?

anonymous · Answer

no it's 500 short

anonymous · Answer

Exactly, so right away A is wrong. Can you tell me which other answers are wrong immediately?

anonymous · Answer

Ohhh ok so I could use this to test my given answers to find the right one! ding dong my light bulb just went on wow I feel dumb. lol

anonymous · Answer

Haha, no worries. So which ones are wrong?

anonymous · Answer

Just from that simple test, which ones are wrong?

anonymous · Answer

ok so my final answers are between b and e

anonymous · Answer

Correct! Good! A, C, and D are all wrong. The 4% values are not 4 times greater than their 6% values. We've eliminated over half the choices!

anonymous · Answer

awesome possum...Now where do I go from there knowing that I have 2 choices of answers

anonymous · Answer

Haha, now we get to look at this:
"borrowed $39,000 to complete a new home."

anonymous · Answer

Can you add the loan values in B and E and tell me if they add up to 39,000?

anonymous · Answer

just kidding the answer is b

anonymous · Answer

sorry Idk why that problem was so hard to wrap my brains around lol thanks for helping me though

anonymous · Answer

Haha, yes! And look, we didn't have to do any hard math at all! You got very lucky xD

anonymous · Answer

Anytime, it's no problem. Would you like to do the math?

anonymous · Answer

This was more test taking strategy.

anonymous · Answer

ha ha true well all the other questions I was working on were hard and I got to this one and was like ok back to basics.. uh oh lol

anonymous · Answer

lol, it happens

anonymous · Answer

It's ok i have it down on my practice paper thanks though!

anonymous · Answer

Happy to help!