A recipe calls for 1 cup of milk for every cups of flour to make a cake that would feed 6 persons. How many cups of both flour and milk will be needed to make a similar cake for 8 people?

Question

Philoid · Accepted Answer

The ratio of number of cups of milk to number of people is constant

When number of cups of milk = 1 number of people are 6

⇒ ratio = = …(i)

When number of people are 8 let number of cups of milk required be ‘a’

⇒ ratio = =

Using (i)

⇒ =

Cross multiply

⇒ a =

Divide numerator and denominator by 2 we get

⇒ a = = = +

⇒ a = 1 + = 1 cups of milk

The ratio number of cups of milk to number of cups of flour is constant

When number of cups of milk is 1 number of cups of flour =

⇒ ratio = = = …(ii)

Let number of cups of flour required be ‘b’ when number of cups of milk are

⇒ ratio = = =

Using (ii)

⇒ =

Cross multiply

⇒ 3b × 2 = 4 × 5

⇒ b =

Divide numerator and denominator by 2

⇒ b = = = +

⇒ b = 3 cups of flour

Therefore, cups of milk needed to make cake for 8 people is 1 and that of flour is 3