Question

on two investments totalling 9000 Lydia lost 4% and earned 5%. if her net receipts were 351$ how much was each investment

Answer 1

She invested.. .say "a" amount on the 4% and "b" amount on the 5% one

now, she lost the 4% one or "a", so... that'd be a negative amount

now, we know both investments added together add up to 9000

and we also know the "net" receipts for the yield was 351, that simply means that whatever "b" and "a" yielded, ended up as 351

so.. what's 4% of a? well (4/100) * a or 0.04a
what's 5% of b? well (5/100) * b or 0.05b

since "a" was a loss(negative), then we know the net yield is =>  b - a = 351

thus     $\bf \begin{cases} b+a=9000\implies \boxed{a}=9000-b\\\\ 0.05b - 0.04a = 351\\ ----------\\ 0.05b - 0.04\left(\boxed{ 9000-b }\right) = 351 \end{cases}$

solve for "b", to see how much was invested at 5%

what about a?  well, a = 9000 - b