how to add fractions with whole numbers

Question

john took al his money from his saving account. he spent $50 on a radio and 3/5 of what was left on present for his friends. John then put 2/5 of his reamining money in to checking account and donated 120$ that wasleft to charity. How much money did john originally have in his saving account?

Answer 1

For each step, we subtract off an amount, for the remaining value.

 

if T = Total $$ to start.   

   ========

 

 T = Total

 

(T - 50)    = remaining after spending $50 on the radio

 

(T - 50) -  (3/5)*(T - 50)  =  remaining amount after 3/5 of remaining is spent on a friend

 

COMBINE TERMS (T) AND REWRITE AS:  

T -50 - (3/5)*T - (3/5)(-50)     =  (2/5)*T  - 50 + 30  =   (2/5)*T - 20    (remaining)

 

So,  (2/5)*T - 20  = remaining amount after 3/5 of remaining on friend  

       ----------------

now subtract 2/5 of this amount to go to a checking account.

What remains in the original acct = $120 which he donates to charity. 

 

so start with the remaining above, and subtract off 2/5 of that amount

(2/5)*T - 20  -  [(2/5)* ((2/5)*T - 20) ]  = 120

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

 

we can now solve for T by combining terms. (T = original $$). 

 

  (2/5)*T - (2/5)*(2/5)*T  - 20  - (2/5)(-20) = 120

  (2/5)*T - (4/25)*T  - 20 - (-8)  = 120

  (6/25)*T  - 12 = 120    

  (6/25)*T = 132        (MULT EACH SIDE BY 25/6)

 

   T = 132*(25/6) = $550    (ORIG AMOUNT)

 

  now, let's check it:

 

   $550 - $50  = $500     (radio $50, remaining is $500)

 

   $500 - (3/5)*500 =  $500- 300   = $200  (remaining is $200, after 3/5 (or $300) spent on present)

 

   $200 - (2/5)*200 =  $200 - $80  = $120  (remaining is $120, after $80 goes to checking)  (this checks)

 

    he now donates the $120.