an individual has two low interest loans, one at 4% interest and the other at 6% interest. The amount borrowed at 6% is $250 more than the amount borrowed at 4% If the total interest for one year is $165, how much money is borrowed at each rate
solve ...
.04x + .06(x+250) = 165
15.04
To determine the amount of money borrowed at each interest rate, we can set up a system of equations.
Let's represent the amount borrowed at the lower interest rate (4%) as 'x'.
According to the problem, the amount borrowed at the higher interest rate (6%) is $250 more than the amount borrowed at 4%. Therefore, the amount borrowed at 6% can be represented as 'x + $250'.
Now, let's calculate the total interest paid for one year. The interest on the loan at 4% is 4% of x, which can be expressed as 0.04x. Similarly, the interest on the loan at 6% is 6% of (x + $250), which can be expressed as 0.06(x + $250).
According to the problem, the total interest for one year is $165. So, the equation becomes:
0.04x + 0.06(x + $250) = $165
Now, we can solve this equation to find the value of 'x'.
0.04x + 0.06x + 0.06($250) = $165
0.1x + $15 = $165
0.1x = $165 - $15
0.1x = $150
To solve for 'x', we divide both sides of the equation by 0.1:
x = $150 ÷ 0.1
x = $1500
Therefore, the amount borrowed at 4% is $1500.
Now, we can calculate the amount borrowed at 6%:
x + $250 = $1500 + $250 = $1750
Therefore, the amount borrowed at 6% is $1750.
To summarize, $1500 is borrowed at a 4% interest rate, and $1750 is borrowed at a 6% interest rate.