Hey <sundarshoba>,

Following are my worked solutions:

Q1.

Two methods can be used to solve this problem, (i) model (ii) simultaneous.

<Simultaneous> method is used here.

P - A = 360 -- (1)

(3/4)P + (1/3)A = 764 -- (2)

(2)x12:

9P + 4A = 9168 -- (3)

Comparing (1),(3) to eliminate A:

(1)x4:

4P - 4A = 1440 -- (4)

Comparing (3),(4):

(3)+(4):

13P = 10608

P = 10608 ÷ 13 = 816 -- (5)

Substitute (5) in (1):

816 - A = 360

A = 816 - 360 = 456

Total dolls at first = P + A

= 816 + 456 = 1272

Given there were 764 dolls left,

number of dolls given away = 1272 - 764 = **508**

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Q2.

*** - for alignment purpose

<Before>

(J + M) : C Total

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

<After>

J : M : C Total

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

As this is an internal transfer process, total sweets (before) = total sweets (after) <Unchanged Total concept>. Hence, common multiple of 7,3 is 21.

(1)x3:

<Before>

(J + M) : C Total

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

(2)x7

<After>

J : M : C Total

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

using <work backwards> method, we have ...

<Jon gave 12 sweets to Molly>

M: 7u - 12

J: 7u + 12

<Chris gave 25 sweets to Jon and 31 sweets to Molly>

<before>

M: 7u - 12 - 31 = 7u - 43 -- (5)

J: 7u + 12 - 25 = 7u - 13 -- (6)

C: 7u + 25 + 31 = 7u + 56 -- (7)

comparing (3),(7):

C:

15u = 7u + 56

8u --> 56

1u --> 56 ÷ 8 = 7

in (6):

J (at first) = 7u - 13 --> (7 × 7) - 13

= 49 - 13 = **36**

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Trust this helps.

Do let me know again if this is different from the <answerkey> or if there's further clarification.

Cheers,

Edward