Question

The number of eggs needed to make a cake varies directly as the number of cups of flour used to make a cake a chef used 2 cups of flour and half a dozen eggs. Write an equation​

Answer 1

Direct variation:

If for any two variables x, y, we find a relation such that when x is increased under a suitable property, y also increases. Same when x is decreased.

Mathematically, we denote this relation as

x ∝ y

In order to form an equation, we introduce a constant k (> 0) which is called constant of variation such that

x = ky

Solution:

Let, the number of flour cups be x and the number of eggs be y to make a cake.

Then by the given condition,

y ∝ x

or, y = kx , where k is constant of variation

Given that, x = 2 and y = 6 (half of a dozen)

Then, 6 = 2k, i.e., k = 3

Therefore, the above relation gives

y = 3x

or, y - 3x = 0

which is the required equation.

Answer 2

Answer:

E=3*C

Step-by-step explanation:

Since six eggs are required for 2 cups of flour, so by dividing 6 by 2 we get 3 which is the proportionality constant. Initially the equation was , E=K*C, where E represents the number of eggs required , k is proportionality constant and C represents number of cups. Now since we have the value of K , we can write this equation as ; E=3*C .