A man invested

Question

10,000 dollars in two business. One business earned 5 percent for the year and another lost 7.5 percent . Find the amount he invested in each business if he earned 25 dollars for the year.

Answer 1

p = the business that earned 5%; q = the business that lost 7.5%

p + q = 10,000

 

A = P*(1 + (r/n))(^{n * t)}

 

Case p:

P = p

r = .05

n = 1

t =1

 

Case q:

P = q

r = -.075

n = 1

t = 1

 

Together:

p(1 + .05/1)^(1*1) + q(1-.075)^(1*1) - 10,000 = 25

1.05p + .925q - 10,000 = 25

1.05p + .925q = 10,025

1.05(10,000 - q) + .925q = 10,025 - (Substitute p from the 2nd line)

10,500 - 1.05q + .925q = 10,025

10,500 - .125q = 10,025

-.125q = -475

q = 3,800

 

p+ q = 10,000

p + 3,800 = 10,000

q = 6,200