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sundarrd

Member

Registered: 2014-01-29

Posts: 2

Fraction word problem

Tom and Jim together have 90 stamps. Tom gave 1/4th of his stamps to Jim then Jim gave 2/5th of his stamps to Tom.
As a result they both have equal amount of stamps. How many stamps did both have initially.

Work out :
Initially Tom had 4 Units . Jim has 5 units after getting 1/4 from Tom.
So the Total of 9 units which is equal to half of the total number of stamps = 45
so 1 unit is 5 .

Tom + Jim = 9+9 =18 Units .  Tom had 4 units = 4 * 5 = 20 stamps
Jim had 14 units = 14 * 5 = 70 stamps.

My question is is there a better way to do this ?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,164

Re: Fraction word problem

hi sundarrd

Welcome to the forum.

Initially Tom had 4 Units . Jim has 5 units after getting 1/4 from Tom.
So the Total of 9 units which is equal to half of the total number of stamps = 45
so 1 unit is 5 .

Tom + Jim = 9+9 =18 Units .  Tom had 4 units = 4 * 5 = 20 stamps
Jim had 14 units = 14 * 5 = 70 stamps.

Using the known answers let's see if that makes sense:

Tom has 4 units so 1 unit = 20/4 = 5.  OK

But you then say Jim has 5 units ?  That's 5 x 5 = 25 stamps.  That's not right.

And why should 4 + 5 = 9 be half the total number of stamps.  As no stamps are lost the sum should always be 90.

I also cannot see where you have used the second exchange information at all.

As you've got to the right answer, I'm guessing that you did it correctly, but haven't exactly described what you did,  here.

Unless a question says you must solve it a certain way, there's nothing wrong with your own method, but make sure you describe it correctly.

Here's my method using algebra:

Let Tom have x stamps.  So Jim has 90 - x

After the first exchange:

Tom has 3x/4 and Jim has 90 - 3x/4

After the second exchange:

Tom has 3x/4 + 2/5 of (90 - 3x/4) and Jim has (90 - 3x/4) - 2/5 of (90 - 3x/4)

Put them equal and multiply by 20 to remove all fractions

30x + 1440 - 12x = 1800 => 18x = 360 => x = 20.

So Tom has 20 and Jim has 70.

check:

first exchange:

Tom has 15 and Jim has 75

second:

Tom has 15 + 30 and Jim has 75 - 30.  These are both 45.  tick.

Bob

Last edited by Bob (2014-01-30 00:18:34)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

sundarrd

Member

Registered: 2014-01-29

Posts: 2

Re: Fraction word problem

Thank you very much Bob .