Question

you invested of $4000 in two stocks that paid 5% and 7% annual interest. at the end of the year, the totally interest from these investments was $230 . how much was invested at each rate?

Answer 1

two investments, say "a" and "b"

so we know you invested $4,000 total for both investments
so \(\bf a+b=4000\)

and we also know that 5% of a and 7% of b yielded an interest of $230

so.... there, you have a system of equations, solve by substitution \(\bf {\color{red}{ 5}}\%\ of \ a=\cfrac{{\color{red}{ 5}}}{100}\times a\implies 0.05a\qquad {\color{red}{ 7}}\%\ of \ b=\cfrac{{\color{red}{ 7}}}{100}\times b\implies 0.07b\\ \quad \\
a+b=4000\\
0.05a+0.07b=230\)