Nico invests some money @ 5%, and $2400 less @4%. Investments total $165.00 in intrest in 1 yr. How much did he invest at each rate?
amount at 5% ---- x
amount at 4% ---- x - 2400
.05x + .04(x-2400) = 165
solve for x
To solve this problem, we can set up a system of equations. Let's assign the following variables:
Let x be the amount of money Nico invested at 5%.
Then, the amount of money he invested at 4% will be (x - $2400).
We know that the total interest earned from both investments is $165. Therefore, we can set up the equation:
0.05x + 0.04(x - $2400) = $165
Now, let's solve the equation step by step:
1. Distribute the 0.04 to get: 0.05x + 0.04x - 0.04($2400) = $165
Simplify: 0.05x + 0.04x - $96 = $165
2. Combine like terms: 0.09x - $96 = $165
3. Add $96 to both sides of the equation to isolate the variable: 0.09x = $165 + $96
Simplify: 0.09x = $261
4. Divide both sides of the equation by 0.09 to solve for x: x = $261 / 0.09
Simplify: x ≈ $2900
Therefore, Nico invested approximately $2900 at 5% and (x - $2400) at 4%. Substituting the value of x, we find:
x - $2400 = $2900 - $2400 = $500.
Hence, Nico invested approximately $2900 at 5% and $500 at 4%.