Hey there,

Q11

(Note: *** - used to buffer whitespace to create alignment; imagine these are all spaces )

Apply <Branching method>

*******|--> 3/4 + 3/4 b (S)

Total -|******************|--> 3/4 + 3/4 b (Y)

*******|--> 1/4 - 3/4 b - |

**************************|--> 1/4 - 3/4 b = 1 b (A)

In other words,

From Total, S = 3/4 + 3/4 b

Remainder (R) = 1/4 - 3/4 b

From R, Y = 3/4 + 3/4 b

Remainder (R1) = 1/4 - 3/4 b

Given that A received the last bead in the bag, then ...

R1 = 1/4 - 3/4 b = 1 b

So, 1/4 = 1 3/4 b

Working Backwards, we have ...

R = 4/4 = (7/4) x 4 = 7 b

So we have ...

R = 1/4 - 3/4 b = 7 b

1/4 = 7 3/4 b

S = 3/4 + 3/4 b

= 3 x (31/4 b) + 3/4 b = 93/4 b + 3/4 b

= 96/4 b = 24 b

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Q12

Cost/Price model:

T |---------------------| } T + G

G |----------|<-------> } = 96

30

G:

96 - 30 = 66

66 ÷ 2 = 33

T:

33 + 30 = 63

Qty / Number ratio:

G : T

3 : 1

So, 3u of G cost $33; 1u of T cost $63.

Hence, 1u of G cost $11.

Comparing the cost of 1u of T and G, the difference is ...

T - G = 63 - 11 = 52

(a)

Given that cost of 1 T is $10.40 more than 1 G,

number of T = 52 ÷ 10.40 = 5

(b)

5G = 11

1G = 11 ÷ 5 = $2.20

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Trust the above helps.

Cheers,

Edward