SOLUTION: A bank loaned Joe $130,000, part of it at the mortgage annual interest rate of 7%, and the rest at the credit card annual interest rate of 19%. The total interest the bank received

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Question 1112196: A bank loaned Joe $130,000, part of it at the mortgage annual interest rate of 7%, and the rest at the credit card annual interest rate of 19%. The total interest the bank received on the loan was $9850. How much was loaned at each rate?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I assume simple interest
+I+=+P%2Ar%2At+
Let +P+ = amount loaned @7%
+130000+-+P+ = amount loaned @ 19%
Let +I+ = interest earned by 7% loan
+9850+-+I+ = interest earned by 19% loan
--------------------------------------------
For 7% loan:
(1) +I+=+P%2A.07%2A1+
For 19% loan:
(2) +9850+-+I+=+%28+130000+-+P+%29%2A.19%2A1+
----------------------------------------
Plug (1) into (2)
(2) +9850+-+.07P+=+24700+-+.19P+
(2) +.12P+=+14850+
(2) +P+=+123750+
and
+130000+-+P+=+130000+-+123750+
+130000+-+P+=+6250+
-------------------------------------------
$123,750 was loaned @7%
$6,250 as loaned @ 19%
-----------------------------------
check:
(1) +I+=+.07P+
(1) +I+=+.07%2A123750+
(1) +I+=+8662.5+
and
(2) +9850+-+I+=+%28+130000+-+P+%29%2A.19+
(2) +9850+-+I+=+%28+130000+-+123750+%29%2A.19+
(2) +9850+-+I+=+6250%2A.19+
(2) +9850+-+I+=+1187.5+
(2) +I+=+8662.5+
OK