Nico is saving money for his college education. He invest some money at 5%, and $1600 less than that amount at 3%. The investments produced a total of $144 interest in 1yr. How much did he invest at each rate?
well, just add it up:
.05x + .03(x-1600) = 144
To solve this problem, let's set up the equations based on the information given.
Let's call the amount Nico invested at 5% A, and the amount he invested at 3% B.
From the problem statement, we know that:
1) The interest earned from the investment at 5% is 5% of A.
2) The interest earned from the investment at 3% is 3% of (A - $1600).
3) The total interest earned from both investments is $144.
Now we can translate these statements into equations:
Equation 1: 0.05A = interest earned from investment at 5%
Equation 2: 0.03(B) = interest earned from investment at 3%
Equation 3: 0.05A + 0.03(B) = $144 (total interest earned)
Let's solve the system of equations to find the values of A and B.
Rewriting Equation 2:
0.03(B) = 0.03(A - $1600) = 0.03A - $48
Substituting this equation into Equation 3:
0.05A + (0.03A - $48) = $144
0.08A - $48 = $144
Adding $48 to both sides of the equation:
0.08A = $144 + $48
0.08A = $192
Dividing both sides of the equation by 0.08:
A = $192 / 0.08
A = $2400
Now that we know A is $2400, we can substitute this value back into Equation 2 to find B:
0.03(B) = 0.03(2400 - $1600) = 0.03 * $800 = $24
So, Nico invested $2400 at 5% and $800 at 3%.