translate the given information into a system of equations.and write the conclusion. the question is below

Question

A man borrowed an interest-free amount from his mother, another amount 10% monthly interest from his brother and another from his friend at 20% monthly rate of interest. due to the interest the original sum of php7000 he borrowed has increased to php8000 after one month. if the amount the man originally borrowed from his friend was twice the amount he borrowed from his brother, find the original amount the man borrowed from his mother,his brother,and his friend.

Answer 1

m + b + f = 7000

 

f = 2b

 

substitute f=2b into the first equation

 

m + b + 2b = 7000

 

m + 3b = 7000

 

the money plus interest charged is this:

 

m + 1.10b + 1.20f = 8000

 

substitute f=2b into that equation

 

m + 1.10b +1.20(2b) = 8000

 

m + 1.10b + 2.40b = 8000

 

m + 3.50b = 8000

 

now subtract m + 3b = 7000

 

 

   m + 3.5 b = 8000

 

-(m + 3b     = 7000)

--------------------------

          .5b   =  1000

 

             b = 2000     this is what he borrowed from his brother

 

f = 2b

 

f = 4000     this is what he borrowed from his friend

 

m + b + f = 7000

 

m + 2000 + 4000 = 7000

 

m = 1000     this is what he borrowed from his mother

 

CHECK:

 

Interest charged = 8000-7000 = 1000

 

10% (loan from brother) + 20% (loan from friend) = 1000

 

.10(2000) + .20(4000) =1000

 

200 + 800 = 1000