Question

Nico is saving money for his college education. He invests some money at 6​%, and ​$1600 less than that amount at 4%. The investments produced a total of ​$156 interest in 1 yr. How much did he invest at each​ rate?

He invested ​$___ at 6​% and ​$___ at 4​%.

Answer 1

let's say the amounts are "a" and "b"
6% 4%

now... we dunno what "a" is, but nevermind, whatever that is, "b" invested at 4%, is 1600 less than that or less than "a", namely b = a - 1600

so.. "a" is the bigger amount than "b" by 1600, but no matter

what is 6% of a? well, 6/100 * a or 0.06a, that's how much it yielded
what is 4% of b? well, 4/100 * b, or 0.04b, that's much it earned in interests

we know, their yield, or total in earned interest is 156, so.. whatever those yields are, they add up to 156 or

0.06a + 0.04b = 156

now
`\bf \begin{cases} \boxed{b}=a-1600\\\\ 0.06a+0.04b=156\\ ----------\\ 0.06a+0.04\left( \boxed{a-1600} \right)=156 \end{cases}`

solve for "a", to see how much was invested at 6%

how much is "b"? well, b = a - 1600