Q1)Shawn packed his storybooks into two boxes, Box A & Box B. He packed 4/5 as many books in Box A as Box B at first. After transferring 16 books from Box B to Box A, there are now 3/4 as many books in Box B as Box A. How many books were there in each Box at first?

Q2)Pete & Amanda share a total of $240. If Pete gives 2/5 of his share to Amanda, and Amanda in turn gives 3/7 of his share to Pete, they will have the same amount of money. How much did each of them have at first?

Q3)A grocer used a basket to hold some flour. At first the empty basket was 1/2 as heavy as the flour. After selling 19kg of the flour, the empty basket becomes 2/5 as heavy as the remaining flour. How many KG of flour did the grocer have at first?

Shawn packed his storybooks into two boxes, Box A & Box B. He packed 4/5 as many books in Box A as Box B at first. After transferring 16 books from Box B to Box A, there are now 3/4 as many books in Box B as Box A. How many books were there in each Box at first?

This is an Internal Transfer question. In these type of questions the total number of storybooks will remain the same before and after. So we need to ensure this is the case with units as well.

Before
A : B
4 : 5 (9units)
28 : 35 (63units)

After
A : B
4 : 3 (7units)
36 : 27 (63units)

8units --> 16
1unit --> 2

At first:
- Box A had 28x2 = 56 books
- Box B had 35x2 = 70 books

Pete & Amanda share a total of $240. If Pete gives 2/5 of his share to Amanda, and Amanda in turn gives 3/7 of his share to Pete, they will have the same amount of money. How much did each of them have at first?

This question also uses the Internal Transfer Concept but there are two steps to process and we need to work backwards.

P : A
1 : 1 (At end)
4 : 4 (At end but with the units being what Amanda has left)
1 : 7 (Before Amanda gave 3/7 to Pete)
3 : 21 (Peter had 3/5 units left so change the units so that Pete has 3)
5 : 19 (At first)

24units --> 240
1unit --> 10

At first
- Pete had $50
- Amanda had $190



A grocer used a basket to hold some flour. At first the empty basket was 1/2 as heavy as the flour. After selling 19kg of the flour, the empty basket becomes 2/5 as heavy as the remaining flour. How many KG of flour did the grocer have at first?

For this question we can use External Unchanged

However, there is a problem with the information provided. You will notice the starting ratio is 1/2 of the flour and the ending ratio is less than 1/2 of the flour. This is not logical as we sold flour and therefore the basket to flour ratio should increase in favour of the basket. Ie The basket should now be more than 1/2.

Before
B : F
1 : 2

After
B : F
2 : 5