Question

Lucas invested money in two accounts: one paying 3% interest and the other paying 5% interest. He invested $100 more in the 5% account than the 3% account. After one year , his total interest from the two accounts was 53$ how much was invested at each rate ?

Answer 1

He invested "a" at 3% and "b" at 5%

now, he invested 100 more in "b", so, whatever "a" may be, b = a + 100

now, how much is the interest yield of each? well
how much is 3% of a? well, (3/100) * a, or 0.03a
and 5% of b? well (5/100) * b, or 0.05b

now, we know the total yield was 53 bucks, thus 0.03a + 0.05b = 53

thus    $\bf \begin{cases} \boxed{b}=a+100\\ 0.03a+0.05b=53\\ ----------\\ 0.03a+0.05\left( \boxed{a+100} \right)=53 \end{cases}$

solve for "a", to see how much was invested at 3%

what about "b"?  well, b = a + 100