Question

John received $9,000 in student loans. Part of the money he was able to borrow at 7% simple interest, but on the rest of the money he was charged 8.25% simple interest. At the end of the year he owed $706.25 in interest. How much did John borrow at each rate.

Answer 1

He borrowed "a" at 7% and "b" at 8.25%

now, whatever "a" and "b" are, we know, his student loan was 9000, thus
a+b = 9000

now, he owes 7% or 7/100 for "a", what's 7% of a? well, 7/100 * a or 0.07a

he owes 8.25% of "b", how much is 8.25% of b? well, 8.25/100 * b or 0.0825b

now, we know, at the end of the year, he owed for both loans, 706.25 in interest
thus we know that 0.07a + 0.0825b = 706.25

thus   $\bf \begin{cases} a+b=9000\implies \boxed{b}=9000-a\\ 0.07a+0.0825b=706.25\\ ----------\\ 0.07a+0.0825\left(\boxed{9000-a} \right)=706.25 \end{cases}$

solve for "a", to see how much he borrowed at 7%

what about "b"? well, b = 9000-a