A mother wants to invest $5,000.00 for her son's future education. She invests a portion of the money in a bank certificate of deposit (CD account) which earns 4% and the remainder in a savings bond that earns 7%. If the total interest earned after one year is $300.00, how much money was invested in the CD account?
let us say, the CD amount she invested is "c"
and the amount she invested in the savings bond is "s"
she invested a total of 5,000
so, whatever "c" is and "s" is, c + s = 5,000
now, the CD account earned 4% in interest
4% in decimal form is 4/100 or 0.04
she also earns 7% from the saving bonds,
7/100 is 0.07
the interest earned after one year are 300
that is, the 4% per year and the 7% per year add up to 300 bucks
so, one can say that
0.04c + 0.07s = 300
\(\begin{cases}
c+s=5,000\to s=\boxed{5,000-c}
\\ \quad \\
0.04c+0.07s=300\to 0.04c+0.07(\boxed{5,000-c})=300
\end{cases}
\\ \quad \\
\textit{solve for "c", or CD amount}\)