Can someone help solve this

Sarah’s two student loans totaled $12,000. One of her loans was at 6% simple interest and the other at 9%. After one year, Sarah owed $855 in interest. What was the amount of each loan?

You have two unknowns, the amount of the 6% loan (we'll call it S for six) & the amount of the 9% loan (we'll call it N for nine). To solve for two unknowns, you need two equations. Write these equations from your sentences above.

"Sarah’s two student loans totaled $12,000" gives us S + N = $12,000

"After one year, Sarah owed $855 in interest" gives us 6%*S + 9%*N = $855, or 0.06S + 0.09N = $855

Solve the first equation for either N or S (doesn't matter, we will do S), then plug that into the second equation & solve that for the remaining variable.

S + N = $12,000
S = $12,000 - N

Now plug that into the second equation

0.06S + 0.09N = $855
0.06($12,000 - N) + 0.09N = $855
$720 - 0.06N + 0.09N = $855
0.03N = $135
N = $135/0.03
N = $4500 <==== First part of answer

Now find S

S = $12,000 - N = $12,000 - $4500 = $7500 <==== Second part of answer

a - the amount of first loan
b - the amount of the second loan

a+b=$12000

I1=a(1+0.06)
I2=b(1+0.09)

I1+I2=855

a+b=12000
1.06a+1.09b=12000+855

a=12000-b

1.06(12000-b)+1.09b=12855
0.03b=135
3b=13500
b=4500
a=7500