Pietro borrows 18 500 Some is from his friend at 1 annual in

Pietro borrows $18, 500. Some is from his friend at 1% annual interest, four times as much as that from his bank at 9%, and the remainder from his insurance company at 15%. He pays a total of $2050 in interest for the first year. How much did he borrow from the bank? (a) List and verbally define your variables, (b) List your facts and/or state your facts in a table. (c) Set - up the appropriate system of equations. (d) Solve the system of equations. Answer the question that is posed in the problem set - up.

Solution

3(a). Let the amount borrowed by Pietro from his friend be $ x. Then the amounts borrowed by him from the Bank and the insurance company are $ 4x and $18500-x-4x = $18000-5x. Then the interest paid by Pietro in the 1st year is x*0.01 + 4x*0.09 + (18500-5x)*0.15= 0.01x +0.36x +2775 -0.75x = 2775-0.38x. Hence, 2775-0.38x = 2050 or, 0.38x = 2775-2050 = 725 so that x = 725/0.38 = $ 1907.89. Then 4x = $7631.56 and $18500-5x = $18500-9539.45 = $8960.55. Thus, Pietro borrowed $ 7631.56 from the Bank.

(b) The only independent variable is the amount borrowed by Pietro from his friend. There are 2 dependent variables, viz. the amounts borrowed by Pietro from the Bank and the insurance company.

From a friend

From Bank

From Insurance Company

Amount borrowed by Pietro($)

1907.89

7631.56

8960.55

Rate of Interest (%)

1

9

15

Amount of Interest ($)

190.79

686.84

1172.37

(c) The required equation is x*0.01 + 4x*0.09 + (18500-5x)*0.15 = 2050 or, 2775-0.38x = 2050, where x is the amount borrowed by Pietro from his friend.

(d) 0.38x = 2775-2050 = 725 so that x = 725/0.38 = $ 1907.89.

	From a friend	From Bank	From Insurance Company
Amount borrowed by Pietro($)	1907.89	7631.56	8960.55
Rate of Interest (%)	1	9	15
Amount of Interest ($)	190.79	686.84	1172.37