Hey there,

Following pls find my worked solutions:

Q1.

<after>

A : B : C

2 : 5 : 9

<process>

A: -(3/5)A

B: +24

C: +(3)C

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

<before>

C: (1/3)C = 9u ÷ 3 = 3u

B: 5u - 24

A: (2/5)A = 2u; (5/5)A = 2 × (5/2) = 5u

Given that total number of stamps in Albums A,B,C was 444 at first, we have ...

<before>

A + B + C = 444

5u + 5u - 24 + 3u = 444

13u --> 444 + 24 = 468

1u --> 36

C - A (end) = 9u - 2u = 7u

7u --> 7 × 36 = **252**

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Q2.

<after>

Js : Jc

1 : 7

Ks : Kc

1 : 4

<process>

J: -12s

K: -18c

<before>

Let the <after> ratio for J be parts(p) and K be units(u).

Js: 1p + 12

Jc: 7p

Ks: 1u

Kc: 4u + 18

Given J bought some chocolates and gave 1/2 of them to K, and K bought some sweets and gave 1/2 of them to J, we have ...

Jc = Kc , and Js = Ks

7p = 4u + 18

1p + 12 = 1u

Rearranging these 2 equations, we have ...

7p - 4u = 18 -- (1)

1u - 1p = 12 -- (2)

As question is asking for number of sweets(s) K bought, we eliminate parts(p) qty as follows:

(2)x7:

7u - 7p = 84 -- (3)

(1)+(3):

7u - 4u = 18 + 84

3u --> 102

1u --> 34

Sweets bought by K (at first) = 2u

2u --> 2 × 34 = **68**

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Q3.

A: (3/8)total + $15

Remainder(R): (5/8)total - 15

Given that B paid $25,

(5/8)total - 15 = 25

(5/8)total = 25 + 15 = 40

Total Cost of present = (8/8)total = 40 × (8/5)

= **$64**

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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