SOLUTION: Tom had 4/5 as many stamps as Michael. After Michael gave away 3/7 of his stamps, Tom had 40 more stamps than Michael. How many stamps did Tom have?

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Question 1187555: Tom had 4/5 as many stamps as Michael. After Michael gave away 3/7 of his stamps, Tom had 40 more stamps than Michael. How many stamps did Tom have?
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52771) About Me  (Show Source):
You can put this solution on YOUR website!
.
Tom had 4/5 as many stamps as Michael. After Michael gave away 3/7 of his stamps,
Tom had 40 more stamps than Michael. How many stamps did Tom have?
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Let 5x be the number of stamps Michael had originally.

Then Tom had  4x stamps originally.


After Michael gave away 3/7 of his stamps, you have THIS equation


    %284%2F7%29%2A%285x%29 = 4x - 40.


To solve, multiply both sides by 7.  You will get


    20x = 28x - 280

    280 = 28x - 20x

    280 =    8x

     x  = 280/8 = 35.


Tom had 4x = 4*35 = 140 stamps originally.    ANSWER

Solved.

Notice that in my solution I introduced the unknown variable in a way to make my computations as simple as possible.



Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

Tom had 4/5 as many stamps as Michael. After Michael gave away 3/7 of his stamps, Tom had 40 more stamps than Michael. How many stamps did Tom have?
Let number Tom had, be T

Then Michael had: 5T%2F4

If Michael gave away 3%2F7, then he had: matrix%281%2C3%2C+%284%2F7%29%285T%2F4%29%2C+%22=%22%2C+5T%2F7%29 remaining 

We then get: matrix%281%2C3%2C+5T%2F7%2C+%22=%22%2C+T+-+40%29

              5T = 7T - 280 ------ Multiplying by LCD, 7

         5T - 7T = - 280

            - 2T = - 280

Original number Tom had. or