Nico is saving money for his college education. He invests some money at 8%, and $1900 less than that amount at 7%. The investments produced a total of $257 interest in 1 yr. How much did he invest at each rate?
0.08*x + (x-1900)*0.07 = 257
0.15 x - 133 = 257
0.15x = 390
x=2600
2600*0.08+700*0.07 = 257. Correct
So the money invested at 8% is 2600, and at 7% is 700.
Let's assume Nico invested x dollars at 8% interest. According to the information given, he invested $1900 less than that amount at 7% interest.
So, the amount invested at 7% interest is (x - $1900).
Now, we can calculate the interest earned from each investment.
The interest earned from the investment at 8% would be (x * 8/100) = 0.08x dollars.
Similarly, the interest earned from the investment at 7% would be ((x - $1900) * 7/100) = 0.07(x - $1900) dollars.
We are given that the total interest earned from both investments is $257.
Therefore, we can set up the equation:
0.08x + 0.07(x - $1900) = $257
Now, let's solve this equation to find the value of x, which represents the amount invested at 8% interest.
0.08x + 0.07x - $133 = $257
0.15x - $133 = $257
0.15x = $390
x = $390 / 0.15
x = $2600
So, Nico invested $2600 at 8% interest.
Now, to find the amount invested at 7% interest:
Amount invested at 7% = $2600 - $1900 = $700.
Therefore, he invested $2600 at 8% interest and $700 at 7% interest.
To solve this problem, we can use a system of equations. Let's take the amount of money Nico invested at 8% as 'x'. According to the problem, he invested $1900 less than that amount at 7%, so the amount invested at 7% can be expressed as '(x - $1900)'.
The interest earned by the money invested at 8% can be calculated using the formula: interest = principal * rate. Therefore, the interest earned at 8% is '0.08x'.
Similarly, the interest earned by the money invested at 7% is '0.07(x - $1900)'.
We are given that the total interest earned is $257. Therefore, we can set up the following equation:
0.08x + 0.07(x - $1900) = $257
Now, let's solve this equation to find the value of 'x', which represents the amount Nico invested at 8%:
0.08x + 0.07x - $133 = $257
0.15x - $133 = $257
0.15x = $390
Dividing both sides of the equation by 0.15, we find:
x = $390 / 0.15
x = $2600
So, Nico invested $2600 at 8%.
To find the amount he invested at 7%, substitute this value of 'x' into the expression '(x - $1900)':
(x - $1900) = ($2600 - $1900) = $700
Therefore, Nico invested $700 at 7% and $2600 at 8%.