Answer: the credit union loaned out $40000 at 6% and $10000 at 12%
Explanation:
Let x represent the amount that the
credit union loaned out at the annual rate of 6%.
Let y represent the amount that the
credit union loaned out at the annual rate of 12%.
credit union loaned out $50,000, part at an annual rate of 6% and the rest at an annual rate of 12%. It means that
x + y = 50000
The interest on $x after 1 year would be
6/100 × x = 0.06x
The interest on $y after 1 year would be
12/100 × y = 0.12y
The collected combined interest was $3,600 that year. It means that
0.06x + 0.12y = 3600- - - - - - - - - 1
Substituting x = 50000 - y into equation 1, it becomes
0.06(50000 - y) + 0.12y = 3600
3000 - 0.06y + 0.12y = 3600
- 0.06y + 0.12y = 3600 - 3000
0.06y = 600
y = 600/0.06
y = $10000
x = 50000 - y = 50000 - 10000
x = $40000