Answer
The answer is: the bank that offers a loan at a 7.5% annual interest loaned Chuck 8000 dollars and the bank that offers a loan at a 6% annual interest loaned Chuck 4000 dollars.
Work Step by Step
We assign the variables:
x = amount loaned by bank A (at 7.5% interest)
y = amount loaned by bank B (at 6.0% interest)
Step 1:
Find the equations that represent the problem.
We can get the first equation from the wording in the problem.
From "Chuck receives loans totaling 12,000 dollars from two banks", we get
$x+y=12000$
If we solve for x, we get:
$x=12000-y$ -> Eq. 1
We can get the second equation from the wording in the problem.
From " One bank charges 7.5% annual interest, and the second bank charges 6% annual interest. He paid 840 dollars in total interest in one year", we get
$0.075x+0.06y=840$ -> Eq. 2
Step 2:
Solve the system of equations. Using the substitution method,
-> Substitute Eq. 1 into Eq. 2
$0.075(12000-y)+0.06y=840$
$900-0.075y+0.06y=840$
$-0.015y=840-900$
$-0.015y=-60$
$y=\frac{-60}{-0.015}$
$y=4000$
-> Substitute the value for $y$ into Eq. 1
$x=12000-4000$
$x=8000$
Step 3:
The answer is: the bank that offers a loan at a 7.5% annual interest loaned Chuck 8000 dollars and the bank that offers a loan at a 6% annual interest loaned Chuck 4000 dollars.
