$11000 was borrowed from two sources, one that charges 15% simple interest and the other that charges 8% simple interest. If the total interest at the end of 1 year was $1510, how much money was borrowed from each source

Let's call the amount borrowed from the source with a 15% interest rate "X" dollars and the amount borrowed from the source with an 8% interest rate "Y" dollars. According to the information given, we can set up two equations based on the simple interest formula: The interest from the first source (15% interest rate) is calculated as 0.15X. The interest from the second source (8% interest rate) is calculated as 0.08Y. We also know that the total interest at the end of 1 year was $1510: 0.15X + 0.08Y = $1510 Now, we are given that the total amount borrowed was $11,000: X + Y = $11,000 We have a system of two equations with two variables: Equation 3: 0.15X + 0.08Y = $1510 Equation 4: X + Y = $11,000 We can use these equations to solve for X and Y. First, let's isolate one of the variables in Equation 4. We'll choose to isolate X: X = $11,000 - Y Now, substitute this expression for X in Equation 3: 0.15($11,000 - Y) + 0.08Y = $1510 Now, distribute the 0.15 on the left side: $1,650 - 0.15Y + 0.08Y = $1510 Combine like terms: $1,650 - 0.07Y = $1510 Subtract $1,650 from both sides: -0.07Y = $1510 - $1,650 -0.07Y = -$140 Now, divide by -0.07 to solve for Y: Y = -$140 / -0.07 Y = $2,000 Now that we know Y, we can find X using Equation 4: X = $11,000 - $2,000 X = $9,000 So, $9,000 was borrowed from the source with a 15% interest rate, and $2,000 was borrowed from the source with an 8% interest rate.