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Sullivan received $\$ 900$ in gift money from his godfather. He wants to invest it into high interest-bearing accounts so he places some of the money in an account earning $7 \%$ simple interest and the rest in an account earning $8.5 \%$ simple interest. At the end of one year, he earned $\$ 73.50$ in interest. How much did Sullivan invest in each account?
He invested $\$$ at $7 \%$ simple interest.
He invested $\$ \square$ at $8.5 \%$ simple interest.
Answer
\(\boxed{\text{Sullivan invested }\$200\text{ in the 7\% simple interest account and }\$700\text{ in the 8.5\% simple interest account.}}\)
Step 1 ：Let the amount invested in the 7\% account be \(x\) and the amount invested in the 8.5\% account be \(y\).
Step 2 ：Write the system of equations: \(\begin{cases} x + y = 900 \\ 0.07x + 0.085y = 73.50 \end{cases}\)
Step 3 ：Solve the system of equations to find the values of \(x\) and \(y\).
Step 4 ：\(x = 200\) and \(y = 700\)
Step 5 ：\(\boxed{\text{Sullivan invested }\$200\text{ in the 7\% simple interest account and }\$700\text{ in the 8.5\% simple interest account.}}\)
