Question

The value of y varies directly with x . If x = 3, then y = 21. What is the value of x when y = 105?

Answer 1

GIVEN :–

• The value of y varies directly with x .

• x = 3 then y = 21.

TO FIND :–

• If y = 105 then value of x = ?

SOLUTION :–

• The value of y varies directly with x .

• We can write this as –

$\\ \implies \bf y \propto x$

$\\ \implies \bf y = kx \: \: \: \: \: \: \: \: \: \: \: \: \: \{ k \to constant\}$

• When x = 3 then y = 21 :–

$\\ \implies \bf 21= k(3)$

$\\ \implies \bf k = \cancel\dfrac{21}{3}$

$\\ \implies \large { \boxed{\bf k = 7 }}$

• Now new equation –

$\\ \implies \bf y = 7x$

• When y = 105 the value of "x" –

$\\ \implies \bf 105= 7x$

$\\ \implies \bf x = \cancel\dfrac{105}{7}$

$\\ \implies \large { \boxed{\bf x=15}}$

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Answer 2

Here, as per the provided question we have find the value of x, when the value of y is 105.

GIVEN :

• The value of y varies directly with x.
• The value of x = 3 and y = 21
• value of y = 105 (2nd case)

TO FIND :

• Value of x = ? (when y is given as 105)

STEP-BY-STEP EXPLAINATION :

The value of y is directly proportional with x

$⟼ \rm {y \: ∝ \: x}$

$⟼ \rm {y \: = \: kx}$

$⟹\rm \: Value \: of \: {x = 3}$

$⟹ \rm { \: Value \: of \: y = 21}$

[ Substituting the values of x and y Here ] –

$⟹ \: 21 = \rm {k}(3)$

$⟹ \rm {k} = \cancel { \frac{21}{3}}$

$⟹ \rm {k \: = 7}$

Now, solving for equation in second case (2nd) –

$⟹ \rm {Value \: of \: y \: = 105}$

[ solving after taking the value for equation as y = 105 (given in second case) and y = 7x (given in first case) –

$⟹ \: 105 = 7 \rm {x}$

$⟹ \rm {x} \: = \cancel { \frac{105}{7}} = 15$

$⟹ \rm {x} = 15$

Therefore, value of x, when value of y is 105 = 15.