SOLUTION: Dana borrowed $8000. She borrowed part of the money from a bank that charged 14% /a interest. She borrowed the remainder from her uncle who charged her 5% /a interest. After 1 year

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Dana borrowed $8000. She borrowed part of the money from a bank that charged 14% /a interest. She borrowed the remainder from her uncle who charged her 5% /a interest. After 1 year      Log On


   

Question 1173931: Dana borrowed $8000. She borrowed part of the money from a bank that charged 14% /a interest. She borrowed the remainder from her uncle who charged her 5% /a interest. After 1 year Dana needed a total of 8850 to repay both loans. How much did she borrow from each source.
Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Dana borrowed $8000.
She borrowed part of the money from a bank that charged 14% /a interest.
She borrowed the remainder from her uncle who charged her 5% /a interest.
After 1 year Dana needed a total of 8850 to repay both loans.
How much did she borrow from each source.
:
Let x = amt borrowed from the bank
total borrowed was 8000, therefore:
(8000-x) = amt borrowed from uncle
:
8850 - 8000 = 850 was the total interest
:
Total interest equation
.14x + .05(8000-x) = 850
.14x + 400 - .05x = 850
.14x - .05x = 850 - 400
.09x = 450
x = 450/.09
x = $5000 borrowed from the bank
then, obviously;
8000 - 5000 = $3000 from the uncle
:
:
Confirm this, find the total of the actual amts
.14(5000) = $700
.05(3000) = $150
-----------------
total int: $850

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


If a formal algebraic solution is not required, here is a quick and easy way to solve two-part "mixture" problems like this.

All $8000 borrowed at 14% would incur $1120 interest.
All $8000 borrowed at 5% would incur $400 interest.
The actual interest was $8850-$8000 = $850.

Look at the three interest amounts $400, $850, and $1120 on a number line and calculate that $850 is $450/$720 = 5/8 of the way from $400 to $1120.

That means 5/8 of the money was borrowed at the higher rate.

ANSWER: 5/8 of the $8000, or $5000, was borrowed from the bank at 14% interest; the other $3000 was borrowed from her uncle at 5% interest.

CHECK: .14(5000)+.05(3000) = 700+150 = 850