1. ## 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.

2. 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

3. b=80, a=40. Thank-you! ^_^

4. Originally Posted by jesuslover
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