Hey <teapot>,

Appreciate you can help provide the <anskey> next time whenever possible. This will help to ease verification. Thank you.

My worked solutions are as follows:

Q1

*** - for alignment purpose

As this is an <Internal Transfer> process, the total number of cards that Sam (S) and Peter (P) had in the end is the same as before (apply <Unchanged Total> concept).

Given each of them had the same number of cards in the end, we have ...

900 ÷ 2 = 450

S ********** P

450 ******* 450

Apply <working backwards> method, we have ...

<After P gave (1/4) of his cards to S>

(3/4)P = 450

(4/4)P = 450 × 4 ÷ 3 = 600

S ********** P

300 ******* 600

<After S gave (1/5) of his cards to P>

(4/5)S = 300

(5/5)S = 300 × 5 ÷ 4 = 375

S ********** P

375 ******* 525

S (at first) = **375** cards

========

Q2

*** - for alignment purpose

<before>

(J + M) : C

** 2 *** : 5

<process>

C gave (25 + 31) sweets to J + M.

J gave 12 to M. {internal transfer between J,M so total remains unchanged}

(J + M): +56

C: -56

<after>

(J + M) : C

** 2 *** : 1

Apply <Changed Qtys> concept and we can use <Cross Multiply> method, we have ...

[(2u + 56) / 2] = [(5u - 56) / 1]

2u + 56 = 2 × (5u - 56)

2u + 56 = 10u - 112

10u - 2u --> 56 + 112

8u --> 168

1u --> 168 ÷ 8 = 21

C (after) = 5u - 56 --> (5 × 21) - 56 = 49

Hence, J (after) = 49 { given each of them had same number of sweets in the end }

<Working backwards>, we have ...

J (before) = 49 + 12 - 25 = **36**

**<< Alternative Method >>**

<before>

(J + M) : C Total

** 2 *** : 5 *** 7 ----- (1)

<process>

C gave (25 + 31) sweets to J + M.

J gave 12 to M. {internal transfer between J,M so total remains unchanged}

(J + M): +56

C: -56

<after>

(J + M) : C Total

** 2 *** : 1 *** 3 ----- (2)

Given that this is an <Internal Transfer> process, we can use <Unchanged Total> concept. hence, we have ...

Lowest common multiple of 7,3 is 21.

<before>

(1)x3:

(J + M) : C Total

** 6 *** : 15 ** 21 ----- (3)

<after>

(2)x7:

(J + M) : C Total

** 14 ** : 7 *** 21 ----- (4)

Given C gave away 56 sweets, we have ...

8u --> 56

1u --> 56 ÷ 8 = 7

C (after) = 7u --> 7 × 7 = 49

Hence, J (after) = 49 { given each of them had same number of sweets in the end }

<Working backwards>, we have ...

J (before) = 49 + 12 - 25 = **36**

======

Trust these help. Do let me know again if these are different from your <anskey> or if there's further clarification.

Cheers,

Edward