Hello <Tping>,

My worked solution is as follows:

This is a typical example of an <Internal Transfer> process {F gave R some chocolate bars and sweets}. Thus we can apply the <Unchanged Total> concept, i.e. the total number of chocolate bars (C) <before> and <after> remains the same. Likewise, the total number of sweets (S).

<before>

FC = 35, FS = 50

RC = 45, RS = 10

Total number of C: 35 + 45 = 80

Total number of S: 50 + 10 = 60

<process>

F gave R some chocolate bars and sweets

<after>

FC : FS

40 : 60

2 : 3

RC : RS

70 : 30

7 : 3

Applying <Unchanged Total> concept, we have ...

<C>

2p + 7u = 80 -- (1)

<S>

3p + 3u = 60 -- (2)

Eliminating (p), we have ...

(1)x3:

6p + 21u = 240 -- (3)

(2)x2:

6p + 6u = 120 -- (4)

(3)-(4):

21u - 6u = 240 - 120

15u --> 120

1u --> 120 ÷ 15 = 8

Hence,

<After>

RC = 7u --> 7 × 8 = 56

RS = 3u --> 3 × 8 = 24

Given that at first,

RC = 45, RS = 10

F gave R:

C: 56 - 45 = 11

S: 24 - 10 = 14

Total given: 11 + 14 = 25

Thus, Frederic gave **25** chocolate bars and sweets altogether to Ryan.

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Trust this helps.

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

Cheers,

Edward