Question

The planning rules for a housing development state that 1/3 of the houses should have three bedroom, 3/8 should have four bedrooms, 1/24 should be executive homes and the rest should have two bedrooms.
A) what fraction of the houses have two bedroom?

B) if 24 houses have two bedrooms, how many houses are on the development?

Answer 1

Answer: a) 1/4; b) 96.

Step-by-step explanation:

a) what fraction of the houses have two bedroom?

$1-\bigg (\dfrac{1}{3} +\dfrac{3}{8} +\dfrac{1}{24} \bigg)=\\\\=1-\bigg (\dfrac{8}{24} +\dfrac{9}{24} +\dfrac{1}{24} \bigg)\\\\=1-\dfrac{18}{24} \\\\=\dfrac{24}{24} -\dfrac{18}{24}= \dfrac{6}{24}=\dfrac{1}{4}$

b) if 24 houses have two bedrooms, how many houses are on the development?

24 houses have two bedrooms - this is 1/4

$24 : \dfrac{1}{4} =96$

Thus, 96 houses are under development.