Fraction word problem

Question

Gavin had a sum of money. He gave 1/2 of it to the African Wildlife Foundation. Then, he gave 1/4 of what he had left to the Amercian Red Cross. Next, he gave the Mercy Corps 1/3 of what he had left. Lastly, he donated 1/2 of what he had to the Global Fund for Women. Gavin was left with $625 in the end. How much money did he have at first?

 

Answer 1

Gavin started with g dollars.

 

Let's do the accounting:

½•g remains after donation to AWF.

one fourth of that then goes to Red Cross, so he has ¾•½•g remaining.

one third of the above then goes to MC so he has (2/3)•¾•½•g remaining after the Mercy Corps donation;

donating to the GFW leaves him, finally, with ½•(2/3)•¾•½•g remaining, and this equals $625.

 

I will let you solve for g.

Answer 2

At beginning amount of money Gavin have = x

 

Donate to African Wildlife Foundation = x/2

 

Donate to Amercian Red Cross. = 1/4(x/2) =x/8

 

Donate to Mercy Corps =1/3(x/8) =x/24

 

Donate to Global Fund for Women. =1/2(x/24) = x/48

 

So Now

 

x/2 +x/8 +x/24 +x/48 +625 = x

 

(24x +6x+2x +x) / 48  + 625 = x

 

33x / 48 + 625 =x

 

x-33x/48  = 625

 

48x -33x = 30000

15x = 30000

x= 2000

 

At beginning amount of money Gavin have = x= $2000