Question

One safe investment pays 10% per year and a more risky investment pays 18% per year. A women who has $138400 to invest would like to have an income of 18720 per year from her investments . How much should she invest at each rate ?

Answer 1

A = amount invested at 10%

b = amount invested at 18%

now, she has 138,400 bucks burning her pockets, so, whatever "a" and "b" are, we know that a + b = 138400.

how much is 10% of a?  well, (10/100) * a, or 0.10a.

how much is 18% of b?  well, (18/100) * b, or 0.18b.

she would like to have an income, namely an interest yield, from her investements of 18720 combined, thus, we know that 10% of a and 18% of b, will need to be that much, thus 0.10a + 0.18b = 18720.

$\bf \begin{cases} a+b=138400\implies \boxed{b}=138400-a\\ 0.10a+0.18b=18720\\ -----------------\\ 0.10a+0.18\left( \boxed{138400-a} \right)=18720 \end{cases} \\\\\\ 0.10a-0.18a+24912=18720\implies -0.08a=-6192 \\\\\\ a=\cfrac{-6192}{-0.08}\implies a=77400$

how much will it be for b?  well, b = 138400 - a.