We know that:
Antrim's Population = 4 × Concord's Population
Antrim's Population = 2 × Bennington's Population
Antrim's Population + Concord's Population + Bennington's Population = 140,000
Let Antrim's Population be x, Bennington's be y, and Concord's be z. Substituting the values in the above equations, we get:
x + y + z = 140,000
We know x = 4 × z and x = 2 × y
Substituting values of y and z in terms of x
x + [tex]\frac{x}{4}[/tex] + [tex]\frac{x}{2}[/tex] = 140,000
⇒ [tex]\frac{7}{4}[/tex] × x = 140,000
⇒ x = 80,000
and y = 80,000 ÷ 2 = 40,000 and z = 80,000 ÷ 4 = 20,000
Hence, Benington's population is y = 40,000
