John runs a florist shop in a small Arkansas town and had to borrow $170,000 to start up the shop. He was able to borrow some from the state business development office at 4% but the rest he had to borrow from a "friend" who charged him 8%. The first year John paid $9800 in interest. How much did he borrow from his friend? How much interest did he have to pay the state development office that year?
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To solve this problem, we can set up a system of equations using the given information.
Let's assume the amount John borrowed from his friend is represented by 'x' (in dollars), and the amount he borrowed from the state business development office is represented by 'y' (in dollars).
According to the problem, the total amount John borrowed is $170,000, so we have the equation:
x + y = 170000 ---(Equation 1)
The interest John paid to his friend is calculated by multiplying the borrowed amount by the interest rate of 8%. Since the interest paid is $9800, we can set up the equation:
0.08x = 9800 ---(Equation 2)
To find the interest paid to the state development office, we can subtract the interest paid to the friend from the total interest paid. So, the interest paid to the state development office is:
Total interest paid - Interest paid to friend = $9800
By solving Equation 2 for 'x', we can find the amount borrowed from the friend:
x = (9800 / 0.08)
Now, let's substitute the value of 'x' in Equation 1 to find 'y':
(9800 / 0.08) + y = 170000
Solving this equation will give us the value of 'y', which represents the amount borrowed from the state development office.
Let's calculate:
x = 9800 / 0.08
x = 122500
Substituting the value of 'x' in Equation 1 to find 'y':
122500 + y = 170000
y = 170000 - 122500
y = 47500
Therefore, John borrowed $122,500 from his friend and $47,500 from the state business development office. The interest paid to the state development office is $9,800.