Question

You invest $15,000 in two funds (stock A and stock B) paying 6.3% and 7.1%

simple interest respectively. The total annual interest is $1050. How much did
you invest in each fund?

Answer 1

a = amount invested at 6.3%

how much is 6.3% of "a"? (6.3/100) * "a", namely 0.063a.

b = amount invested at 7.1%

how much is 7.1% of "b"? (7.1/100) * "b", namely 0.071b.

we know the total amount invested is $15,000, so whatever "a" and "b" might be, we know that a + b = 15000.

we also know that the yielded amount in interest is $1050, so if we simply add their interest, that'd be 0.063a + 0.071b.

`\begin{cases} a + b = 15000\\ b = 15000 - a\\[-0.5em] \hrulefill\\ 0.063a+0.071b=1050 \end{cases} \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{0.063a+0.071(\underset{b}{15000-a})=1050}\implies 0.063a+1065-0.071a=1050 \\\\\\ 0.063a-0.071a=-15\implies -0.008a=-15\implies a=\cfrac{-15}{-0.008} \\\\\\ \boxed{a = 1875}\hspace{15em}\boxed{\stackrel{15000~~ - ~~1875}{b = 13125}}`