Question

In planning her retirement, Liza deposits some money at 2% interest, twice as much deposited at 2.5%. What is the amount deposited at each rate if the total annual interest income is $1190?

Answer 1

She deposited two amounts, let's say "a" and "b"
"a" earning 2% interest
"b" earning 2.5% interest

the 2.5% one, is twice as much as the 2% one
so.. one can say that, whatever "a" is, "b" is twice as much,
or b = 2*a -> b = 2a

now.. .the sum of both earned interest, was $1190

so.. one can say that (2% of a) + (2.5% of b) = 1190
let' us use the decimal notation then
$\frac{2}{100}a+\frac{2.5}{100}b=1190\implies 0.02a+0.025b=1190 \\ \quad \\ \textit{however, we know "b" is 2a thus} \\ \quad \\ 0.02a+0.025\boxed{b}=1190\implies 0.02a+0.025(\boxed{2a})=1190$

solve for "a" to find what the "a" amount is,
to find "b", well, "b" is "2a", so just do a 2*a to get "b"