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%.

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      

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

how much is "b"?  well, b = a - 1600

First step is to get rid of the square root. remember that a square root is the same as raising to the (1/2) power. see below: multiply exponents per exponent rules to get: remember you subtract exponents from the denominator and add exponents in the numerator so: simplify further: so a is the correct choice. if you don't understand this google exponent rules and it will you understand. look at the image results.