4) a)simplify each of the folowing ratios (i)a:b=1 1/2 : 2 2/5 (ii)b:c= 0.105 : 0.350 b)Hence,find the ratio a:b:c c) Alan,Bob and Cathy share $5000 in the rati

Question No. 4
a. (i) a : b
[tex]a:b=1 \frac{1}{2}:2 \frac{2}{5} \\ \\ = \frac{3}{2}: \frac{12}{5} ....likened\ the\ denominator\ to\ 10\\ \\= \frac{15}{10}: \frac{24}{10}... both\ sides\ multiplied\ with\ 10 \\ \\ =15:24=5:8 [/tex]
 
a. (ii) b : c
[tex]b:c=0,105:0,350 ... both\ sides\ multiplied\ with\ 1000\\ \\ = 105: 350 ...... both\ sides\ devided\ with\ 35\\ \\= 3:10 [/tex]

b. Ratio of a : b : c
a : b₁ = 5 : 8
b₂ : c = 3 : 10

a : b : c = (a × b₂) : (b₁ × b₂) : (b₁ × c)
a : b : c = (5 × 3) : (8 × 3) : (5 × 10)
a : b : c = 15 : 24 : 50

c. 15 + 24 + 50 = 89

[tex]Alan = \frac{15}{89} \times 100 \% \\ \\Alan = 0,1685 \times 100 \% \\ \\ Alan= 16,85 \% [/tex]

Question No. 5
The monthly salary of Paula = P
The monthly salary of Tom = T

P : T = 5 : 9
T = ⁹/₅ P

T = P + $3200

⁹/₅ P = P + $3200
⁹/₅ P - P = $3200
⁹/₅ P - ⁵/₅ P = $3200
⁴/₅ P = $3200
P = $3200 × ⁵/₄
P = $800 × 5
P = $4.000

Question No. 6
Deposit = $3800
Interest = 3% p.a

a. Simple interest for 4 years = Deposit × interest × time
SI = $3800 × 3% × 4
SI = $38 × 12
SI = $456

b. If SI = $171, time of Deposit = ?
$171 = $3800 × 3% × t
$171 = $114 × t
t = $171 ÷ $114
t = 1,5 ...........The time of deposit is 1,5 years

Question No. 7
The annual value of shop = $36.000
Property Tax Rate = 10%
 
The Amount of Property Tax = The Value × Tax Rate
The Amount of Property Tax =  $36.000 × 10%
The Amount of Property Tax =  $3.600


***Hopefully Helped***