SOLUTION: A bank loaned out ​$19,000​, part of it at the rate of 7% per year and the rest at per 17% year. If the interest received in one year totaled ​$2500​, how much was loaned

Algebra.Com
Question 1196177: A bank loaned out ​$19,000​, part of it at the rate of 7% per year and the rest at per 17% year. If the interest received in one year totaled ​$2500​, how much was loaned at 7%?
Answer by ikleyn(52756)   (Show Source): You can put this solution on YOUR website!
.
A bank loaned out ​$19,000​, part of it at the rate of 7% per year and the rest at per 17% year.
If the interest received in one year totaled ​$2500​, how much was loaned at 7%?
~~~~~~~~~~~~~~~ 

Let x be the amount (in dollars) loaned at 17%.

Then the amount loaned at 7% is (19,000-x) dollars (the rest).


Having it, write the money equation for the combined annual interest

    0.17x + 0.07*(19000-x) = 2500  dollars.


Simplify and find x

    0.17x + 1330 - 0.07x = 2500

    0.17x - 0.07x = 2500 - 1330

        0.1x      =    1170

            x     =  = 11700.


ANSWER.  $11700 was loaned at 17%,  the reast  19000 - 11700 = 7300 dollars was loaned at 7%.

CHECK.   0.17*11700 + 0.07*7300 = 2500 dollars, total annual interest.   ! Correct !

Solved.

----------------------

It is a standard and typical problem on investments/loaning.

If you need more details,  or if you want to see other similar problems solved by different methods,  look into the lesson
    - Using systems of equations to solve problems on investment
in this site.

You will find there different approaches  (using one equation or a system of two equations in two unknowns),  as well as
different methods of solution to the equations  (Substitution,  Elimination).

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic  "Systems of two linear equations in two unknowns".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.



RELATED QUESTIONS

A bank loaned out $16,000, part of it at the rate of 7% per year and the rest at 17% per... (answered by richwmiller)
a bank loaned out $13000, part of it at the rate of 7% per year and the rest at 17% per... (answered by richwmiller)
A bank loaned out $14,000, part of it at the rate of 9% per year and the rest at 19% per... (answered by rfer)
A bank loaned out $14,000, part of it at the rate of 9% per year and the rest at 17% per... (answered by stanbon)
A bank loaned out ​$16 comma 000 ​, part of it at the rate of 7 % per... (answered by addingup,josmiceli)
Please help me solve this problem. A bank loaned out ​$16000, part of it at the... (answered by math_helper)
a bank loaned out 12000 part of it at the rate of 8 per year and the rest at 18% per... (answered by ewatrrr)
A bank loaned out ​$18000, part of it at the rate of 6% per year and the rest at... (answered by ikleyn,greenestamps,MathTherapy)
A bank loaned out ​$14,000​, part of it at the rate of 8 % per year and the rest at... (answered by ikleyn)