
Appreciate any help. Thank you
Appreciate any help. Thank you
Your solution using total unchanged method is correct.
Alternative method:
We know at the beginning Calvin has 4 units.
Then we know at the end, what’s left for each person is as follows:
Calvin [3 units of Calvin][1 part of Susie] = 45
Susie [4 parts of Susie] = 36
If 4 parts of Susie = 36, 1 part of Susie = 9.
3 units of Calvin = 45 – 9 = 36
Hence 4 units of Calvin at the beginning = 48
Is it correct?
Yes! Your answer is correct.
The working can perhaps be simplified. Just focus on the movement of +/- 9 and +/- 12 cards. Seems more natural for the problem. (Just my opinion.)
Calvin | Susie | Logic |
45 | 36 | 36 is 4/5 of Susie’s cards; so she gave 36/4 = 9 to Calvin |
45 – 9 = 36 |
36 + 9 = 45 |
36 is 3/4 of Calvin’s cards; so he gave 36/3 = 12 to Susie |
36 + 12 = 48 |
45 – 12 = 33 |
Calvin had 48 cards at first. |
The total sum of 81 is not quite necessary in the working – but no harm tracking it as it is useful for sanity check.
After Susie gave 1/5 of her cards to Calvin, she left with 36 cards.
So Susie left with 4/5 of her cards after giving.
Susie has 5/4 * 36 = 45 cards before giving.
Calvin has 45 cards after Susie gave 1/5* 45 = 9 cards to him.
So he has 45-9=36 cards before giving 1/4 of his cards to Susie.
Or Calvin has 4/3* 36 = 48 cards at first.
Checking:
Susie has 45 cards after receiving 1/4 * 48 = 12 cards Or Susie has 45-12=33 cards at first.
Calvin Susie
First 48 33
After Calvin gave of his cards to Susie 3/4 * 48 = 36 33 + (1/4 *48 )=45
After Susie gave of his cards to Calvin 36 + (1/5 * 45) =45 4/5 * 45 = 36