A man has a certain number of chicken and goats. Their head count is 30. If the total number of their legs is 84. What is the ratio between the number of chickens and goats ?

Correct option is A

Let x = Number of chickens (2 legs)
Let y = Number of goats (4 legs)
System of Equations:
​$$x + y = 30 \quad (1) \\2x + 4y = 84 \quad (2) \\$$​​
Isolate x from (1):
​$$x = 30 - y \quad (3) \\\\$$​​
Substitute (3) into (2):
​$$2(30 - y) + 4y = 84 \\60 - 2y + 4y = 84 \\60 + 2y = 84 \\\\$$​​
Solve for y (Goats):
​$$2y = 84 - 60 \\2y = 24 \\y = \frac{24}{2} \\y = 12 \\\\$$​​
Substitute y=12 back into (3) to find x(Chickens):
​$$x = 30 - 12 \\x = 18 \\\\$$​​
Calculate the ratio of chickens to goats (x:y):
Ratio = $$\frac{x}{y} = \frac{18}{12} \\$$​​
Ratio = $$\frac{18 \div 6}{12 \div 6} \\$$​​
Ratio = $$\frac{3}{2} \text{ or } 3:2 \\$$​​