Question

Today is Rini’s birthday. Mama is making a beautiful cake

for her. Rini wants to learn from her mother. Mother is very

happy. She takes a cup and some eggs. She said the number of eggs needed to make a cake varies directly as the number of cups of flour used. She takes 2 cups of flour and a half a dozen eggs. As number of guests increase, the number of eggs and cups of flour increase. Take ‘x’ as the number of cups of flour used and ‘y’ as the number of eggs.


(a) Write an equation for the above relationship.

(i) y = 3x (ii) y = 2x (iii) y = 6x (iv) y = 13x

(b) How many eggs are needed if you take 3 cups of flour?

(i) 7 eggs (ii) 8 eggs (iii) 9 eggs (iv) 5 eggs

(c) How many cups of flour needed if Rini takes 21 eggs?

(i) 7 cups (ii) 8 cups (iii) 9 cups (iv) 6 cups

(d) Will the point (2, 6) lie on the graph y = 3x?

(i) always lie (ii) never lie

(iii) may lie (iv) may or may not lie

(e) If (1,3) is solution of the equation y – 3x = 0, then the graph of this equation

(i) passes through the origin. (ii) is parallel to the x-axis.

(iii) is parallel to the y-axis. (iv) lies on the graph.​

Answer 1

Given :- The number of eggs needed to make a cake varies directly as the number of cups of flour used. She takes 2 cups of flour and a half a dozen eggs. As number of guests increase, the number of eggs and cups of flour increase. Take ‘x’ as the number of cups of flour used and ‘y’ as the number of eggs.

To Find :-

(a) Write an equation for the above relationship ?

(i) y = 3x (ii) y = 2x (iii) y = 6x (iv) y = 13x

(b) How many eggs are needed if you take 3 cups of flour ?

(i) 7 eggs (ii) 8 eggs (iii) 9 eggs (iv) 5 eggs

(c) How many cups of flour needed if Rini takes 21 eggs ?

(i) 7 cups (ii) 8 cups (iii) 9 cups (iv) 6 cups

Solution :-

we have ,

• x = Number of cups .
• y = Number of eggs .
• y ∝ x .

so,

→ y ∝ x

→ y = k * x ( where k is a constant number.)

putting y = 2 cups and x = half a dozen = 6 eggs .

→ 2 = k * 6

→ k = 3

then,

→ y = k * x

→ y = 3x (i) (Ans.A)

also, when x = 3 cups,

→ y = k * x

→ y = 3 * 3

→ y = 9 eggs .(ii) (Ans.B)

and, when y = 21 eggs ,

→ y = k * x

→ 21 = 3 * x

→ x = 7 cups. (i) (Ans.C)

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Answer 2

Answer:

a) y=3x

b) 9 eggs

c) 7cups

d) always lie

e) is parallel to y- axis

Step-by-step explanation:

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