Algebra word problem help, please?

Question

Bob invested $20,000, part at 14% and part at 13%. If the total interest at the end of the year is $2,720, how much did he invest at 14%?

Could someone please help me get this started? I am on my last week of algebra and am just trying to do the best I can to finish? Thank you so much. I am having such a hard time.

Answer 1

The total invested is $20,000.

The part he invested at 14% can be represented as a.

Therefore, the rest of the $20,000 was invested at 13%. This can be represented by 20,000-a

His total interest was 2,720 so

2,720 = (.14 x a) + (.13 x (20000-a))

Solve for a...that will be the amount invested at 14%

I hope this helps.
I apologize for the confusing equation. There are some limitations to typing algebraic equations into a computer.

Answer 2

I can't remember how to solve it exactly...so I just guessed and checked till it came out right.
Bob had 20,000 which he invested at different rates resulting in an annual interest gain of 2720.
So I multiplied $12,000 x .14 and got $1,680. Then I multiplied the remaining portion of the 20,000 by .13. That is $8,000 x .13 = $1,040. The total interest is $2,720. Add the interest to the initial $20,000 and you have a total of $22,720. So the answer is that Bob invested $12,000 at .14 and $8,000 at .13. Hope this helps.

Answer 3

I used the "empirical method" for solving the problem.

If the entire $20,000 was invested at 13%, the interest = $2600.
If the entire $20,000 was invested at 14%, the interest = $2800.
It appears more than 50% of the money was invested at 14%.

After a little trial and error, I came up with the correct answer.

$8,000 * 13% = $1,040.
$12,000 * 14% = $1,680.
$1,040 + $1680 = $2,720.

This method won't fly with your algebra teacher, because it doesn't use a formula, but it's the right answer.

P.S. - Vambu_Vaishu and Mr. G have the correct approach to solving the problem algebraically.

Answer 4

let the amt he invested at 14% be 'x'. therefore, the amt invested at 13% would be (20000-x)

Total interest= [14*x + 13(20,000-x)] /100 = 2720

now simplify that..

The key is to work from the question... it asks u wat the amt investd at 14% is.. so that's ur unknown, put it as 'x'

Answer 5

mmm... dad said it can be counted, but he said he's tired of counting investment and interests. try ask your dad? :)

Answer 6

wait, wouldnt u want to divide it by 13%. i did this last yr, but i 4got. :)

Answer 7

answer is $ 12000