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 = 1

3

x

(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

SOLUTION

TO DETERMINE

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 = 1/3x

(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.

EVALUATION

Here it is given that

‘x’ as the number of cups of flour used and ‘y’ as the number of eggs.

So by the given condition

$\sf{y \propto x}$

$\sf{ \implies \: y = k x}$

Now She takes 2 cups of flour and a half a dozen eggs

So x = 2 & y = 6

$\sf{ \implies \: 6 = 2k}$

$\sf{ \implies \: 2k = 6}$

$\sf{ \implies \: k = 3}$

Hence the required equation is y = 3x

(a) The equation for the above relationship.

(i) y = 3x

(b) Now she take 3 cups of flour

Which gives x = 3

∴ y = 3 × 3 = 9

The eggs are needed if you take 3 cups of flour

(iii) 9 eggs

(c) Now y = 21

which gives

3x = 21

∴ x = 7

The number cups of flour needed if Rini takes 21 eggs

(i) 7 cups

(d) Since 6 = 3 × 2

So (2,6) lies on y = 3x

The the point (2, 6) lie on the graph y = 3x

(i) always lie

(e) Since 3 - ( 1 × 3 ) = 3 - 3 = 0

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

(iv) lies on the graph

━━━━━━━━━━━━━━━━

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Answer 2

Answer :

i. y = 3x

ii. 9eggs

iii. 7cups

iv. always lie

v. lies on the graph