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 Question from marina, a parent: I have a bag of gold coins. I give 1/8 to mother then gave 1/2 of what was left to my brother i give 2/7 of what was left to father. If i have 25 coins left. how many do i have originally.

We have two responses for you

Mirina,

I can get you started on this problem. The technique I am going to use is to work backwards. I'm going to keep track with a table.

Number of coins before Action
she gave 1/8 to her mother
she gave 1/2 to her brother
she gave 2/7 to her father
25 coins left

The last step was to give 2/7 of the coins that were left to your father leaving you with 25 coins. Since at that stage you gave away 2/7 of your coins then you kept 1 - 2/7 = 5/7 of the coins. Hence 5/7 of the coins is 25 coins. If 5/7 of your coins is 25 coins then 1/7 is 5 coins and 7/7 is 35 coins. Hence before giving coins to your father you had 35 coins.

Number of coins before Action
she gave 1/8 to her mother
she gave 1/2 to her brother
35 she gave 2/7 to her father
25 coins left

Check:

You had 35 coins. 2/7 of 35 is 2/7 × 35 = 10 and hence you gave 10 coins to your father leaving you with 25 coins.

How many coins did you have before you gave 1/2 to your brother?

Penny

Rewrite each of the gifts in terms of what was kept: "I gave some to my mother, keeping 7/8. Then I gave some of what I had then to my brother, keeping 1/2. Then..."

So if the four quantities are A [original] B [after the first gift], C, and D, you have

B = 7/8 A, C = ??? x B, and so on.

You should be able to combine these to get D as a fraction times A. But you know D = 25.

Another way to do this problem is to work through it backwards.

[a]
I give 2/7 of what was left to father.
I have 25 coins left.

How many do you have at time [a]?
Fill it in below

[b]
then gave 1/2 of what was left to my brother

[a: I have ____________coins]

So how many at time [b]? Fill it in below.

I have a bag of gold coins. [c]
I give 1/8 to mother
[b: I have ____________coins]

So how many at [c]?

Good Hunting!
-RD

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