Solve the following problems related to ratios and shares.
(a) Simplify the given ratios:
(i)
[tex]\[
4: 4 = 1 \frac{1}{2} \div 2 \frac{2}{3} = 1 \frac{5}{2}: 2 x^2 = \frac{3 \pi}{42}, \frac{12}{52} = \frac{15}{15}: \frac{24}{10} = 0.5: \frac{10}{8} \alpha + 3
\][/tex]
(ii)
[tex]\[
6:c = 0.105:0.50 = xa70.105:0.389 \times 1000 = 3105: 350 \quad 1 \div 35
\][/tex]
(b) Hence, find the ratio of [tex]\(a: b: c\)[/tex]:
[tex]\[
a: b: c = x a 5: 5: 3 = 15: 2 + \div 50
\][/tex]
(c) Alan, Bob, and Cathy share [tex]\(\$ 500\)[/tex] in the ratio [tex]\(a: b: c\)[/tex] found in (b). Find Alan's share, correct to the nearest cent.