Appreciate any help. Thank you

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# Question

# Answer

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

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