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Set up a system of linear equations to represent the scenario. Solve the system by using Gaussian elimination or Gauss-Jordan elimination. Assume the interest rates are annual. Latoya borrowed $19,500 to buy a truck for her business. She borrowed from her parents who charge her 5% simple interest. She borrowed from a credit union that charges 4% simple interest, and she borrowed from a bank that charges 3% simple interest. She borrowed four times as much from her parents as from the bank, and the amount of interest she paid at the end of 1 yr was $870. How much did she borrow from each source

Respuesta :

Answer:

p = $12,000

c = $4,500

b = $3,000

Step-by-step explanation:

Denote the variables as follows:

p = amount borrowed from parents

c = amount borrowed from the credit union

b = amount borrowed from the bank

The equations that can be formed using the given information are as follows:

p + c + b = 19500... (i)

p = 4b... (ii)

The formula to compute simple interest is:

SI = P × (R/100) × T

So, the equation for the total interest paid at the end of 1 year is:

0.05p + 0.04c + 0.03b = 870

5p + 4c + 3b = 87000... (iii)

Substitute (ii) in (i) and (iii) and simplify as follows:

4b + c + b = 19500

⇒ c + 5b = 19500... (iv)

5(4b) + 4c + 3b = 87000

⇒ 4c + 23b = 87000... (v)

Subtract (iv) from (v):

4c + 23b = 87000

(-)c + (-)5b = (-)19500 ] × 4

⇒

4c + 23b = 87000

-4c - 20b = -78000

⇒

3b = 9000

b = 3000

Compute the value of p as follows:

p = 4b = 4 × 3000 = 12000

p = 12000

Compute the value of c as follows:

p + c + b = 19500

12000 + c + 3000 = 19500

c + 15000 = 19500

c = 4500

Thus, the amount borrowed from each source is:

p = $12,000

c = $4,500

b = $3,000

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