Question

A mother wants to invest $8000 for her children's education. She invests a portion of the money in a bank certificate of deposit which earns 4% and the remainder in a savings bond that earns 7%. If the total interest earned after one year is $480, how much money was invested at each rate?

Answer 1

She invested "a" at 4% and "b" at 7%

now, how much is 4% of a? well  4/100 * a or 0.04a

how much is 7% of b? well 7/100 * b, or 0.07b

now, we know their interest yield was 480, thus

0.04a + 0.07b = 480

we also know, she had 8000 to invest and split it in two investments, so
a + b = 8000

now   $\bf \begin{cases} a+b=8000\implies \boxed{b}=8000-a\\ 0.04a+0.07b=480\\ ----------\\ 0.04a+0.07\left( \boxed{8000-a} \right)=480 \end{cases}$

solve for "a" to see how much she invested at 4%

what about "b"?  well b = 8000 - a