Answer:
principal of first loan = $7,000
principal of second loan = $5,000
Step-by-step explanation:
Let x = principal of first loan
Let y = principal of second loan
Given:
- Interest rate on first loan = 8% = 0.08
- Interest rate on second loan = 9% = 0.09
- Total amount of interest paid = $1,010
Create two equations with the given information:
Equation 1: x + y = 12000
Equation 2: 0.08x + 0.09y = 1010
Rewrite Equation 1:
⇒ x = 12000 - y
Substitute into Equation 2 and solve for y:
⇒ 0.08(12000 - y) + 0.09y = 1010
⇒ 960 - 0.08y + 0.09y = 1010
⇒ 0.01y = 50
⇒ y = 5000
Substitute found value of y into Equation 1 and solve for x:
⇒ x + 5000 = 12000
⇒ x = 7000
