SOLUTION: Hi Amy has 25% as many marbles as Ben. After Ben gave some marbles to Amy,Amy now has 3/7 as many marbles as Ben. What fraction of the marbles that he had at first did Ben give to

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Question 1206039: Hi
Amy has 25% as many marbles as Ben. After Ben gave some marbles to Amy,Amy now has 3/7 as many marbles as Ben. What fraction of the marbles that he had at first did Ben give to Amy.
Thanks
Found 2 solutions by math_tutor2020, greenestamps:
Answer by math_tutor2020(3816) (Show Source):
You can put this solution on YOUR website!

b = number of marbles Ben started with
0.25b = number of marbles Amy started with

g = number of marbles Ben gives to Amy
b-g = number of marbles Ben has left after giving those marbles
0.25b+g = number of marbles Amy has after receiving those marbles

It might be helpful to organize the information into a table such as this.

Ben Amy
Old b 0.25b
New b-g 0.25b+g

The table is optional.

After Ben gave some marbles to Amy, Amy now has 3/7 as many marbles as Ben
(3/7)*(Ben's new count) = Amy's new count
(3/7)*(b-g) = 0.25b+g

The question "What fraction of the marbles that he had at first did Ben give to Amy?" is asking us to determine g in terms of b.

Specifically the template we want is: g = (some fraction)*b

That means we'll need to solve the equation above for g.
(3/7)*(b-g) = 0.25b+g
7*(3/7)*(b-g) = 7*(0.25b+g)
3(b-g) = 1.75b+7g
3b-3g = 1.75b+7g
3b-1.75b = 7g+3g
1.25b = 10g
g = 1.25b/10
g = 0.125b
g = (125/1000)*b
g = (1/8)*b

The last equation tells us that Ben gave 1/8 of his initial count of marbles to Amy.

There isn't enough information to determine how many marbles each person has (there are infinitely many possibilities). But let's look at one possible example.

Let's say Ben started with 400 marbles.
25% of 400 = 0.25*400 = 100 marbles is what Amy started with.

If Ben gives 1/8 of his marbles to Amy, then he'll hand over (1/8)*400 = 50 marbles to her.
Ben = 400 - 50 = 350
Amy = 100 + 50 = 150
Then form a ratio of these new updated counts.
150/350 = (3*50)/(7*50) = 3/7
which shows that Amy has 3/7 as many marbles compared to Ben.
This example hopefully illustrates why the answer works. Feel free to try other starting marble counts for Ben.

Answer: 1/8

Answer by greenestamps(13196) (Show Source):
You can put this solution on YOUR website!

Given that Amy has 1/4 as many marbles as Ben...

let x = # Amy has at first
then 4x = # Ben has at first

Ben gives some number n of marbles to Amy:

x+n = # Amy now has
4x-n = # Ben now has

The number Amy now has is 3/7 of the number Ben has:

The number of marbles Ben gave to Amy is (1/2)x; the number he started with was 4x. The fraction of his marbles that he gave to Amy is

ANSWER: 1/8