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  1. #1
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    word problem help

    The question:

    A had 3 times as many books as B. A sold B 50 books; then B had twice as many as A. How many books had each then?

    Both my dad and I put our heads together and we couldn't figure out the correct answer. Could someone help me write it out? Thank-you.
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  2. #2
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    Hello,

    I'll try to put mine then

    Let a and b be the number of books of A and B.

    A had 3 times as many books as B.
    This means that a=3b

    A sold B 50 books
    So we're working on a-50 and b+50 because a gave 50 books and b received 50 !

    then B had twice as many as A
    -> "number of books now B have is twice number of books A now have"

    This means that (b+50)=2(a-50)



    Now, you have to solve for a and b with the two equations :

    a=3b
    b+50=2(a-50)

    You can work with substitutions, the most expeditive way imho
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  3. #3
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    b=80, a=40. Thank-you! ^_^
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  4. #4
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    Quote Originally Posted by jesuslover View Post
    The question:

    A had 3 times as many books as B. A sold B 50 books; then B had twice as many as A. How many books had each then?

    Both my dad and I put our heads together and we couldn't figure out the correct answer. Could someone help me write it out? Thank-you.
    Let the number of books A had be a ( hehe ) and let the number of books B had be b ( lol be b )

    Case 1:- A had 3 times as much as books B had

    so, a=3b ---------> equation 1

    Case 2:- A sold 50 books to B because of which B has twice the amounts of book A had,

    A sold 50 books so , the number of books A will have is a-50 ( becasue she gave the books )

    B got 50 books so then number of books B will have is b+50 ( he got the damn books )

    SO now we get the equation

    b+50=2(a-50) ---------> Equation 2
    this implies b+50 = 2a - 100
    b = 2a - 150 -----------> equation 3

    From equation 1, a= 3b substituting in equation 3 we get

    b = 2(3b) - 150
    b = 6b - 150
    5b = 150
    b = 30
    therefore B had 30 books and A had 90 ( since a=3b )

    And thats that, you can say hi to your dad from me

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