1. ## Confusing Word Problem

If anyone could me figure out this problem I would greatly appreciate it. I think I started right but I'm a little lost.

Cole's two student loans totaled $31,000. One of his loans was at 2.8% simple interest and the other at 4.5%. After one year, Cole owed$1024.40 in interest. What was the amount of each loan?

If anyone could me figure out this problem I would greatly appreciate it. I think I started right but I'm a little lost.

Cole's two student loans totaled $31,000. One of his loans was at 2.8% simple interest and the other at 4.5%. After one year, Cole owed$1024.40 in interest. What was the amount of each loan?

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Let ( X )be the loan amount with 2.8% interest rate.
Let (31,000-X) be the loan wity 4.5%.
So put these together equation will come out like this
( X * 2.8% ) + ( 31000-X) * 4.5% = 1024.4
X= 21800 which is the loan amount with 2.8% int rate.
31000-21800 = 9200 will be the loan amount wity 4.5%.
you can back test with answer as follow
21800 @ 2.8% = 610.40
9200 @ 4.5@ = 414
610.40 + 414 = 1024.4 so answer is correct

Cole's two student loans totaled $31,000. One of his loans was at 2.8% simple interest and the other at 4.5%. After one year, Cole owed$1024.40 in interest.
What was the amount of each loan?

Let $\displaystyle x$ = amount at 2.8%
. . This cost him: .$\displaystyle 0.028x$ dollars in interest.

Then the rest, $\displaystyle 31,\!000-x$ = amount at 4.5%
. . This cost him: .$\displaystyle 0.045(31,\!000-x)$ dollars in interest.

His total interest charge was: .$\displaystyle 0.028x + 0.045(31,\!000-x)$ dollars.

But we are told that his total interest charge was: $1024.40. There is our equation! . . . . .$\displaystyle {\color{blue}0.028x + 0.045(31,\!000-x) \;=\;1024.40}\$