Question

CHALLENGE FOR ALL MATH LOVING BRAINLIANS !!


GIVEN :
$\large \boxed{ \sf {5 \frac{3}{ x} \times y\frac{1}{2}} = 19}$


TO FIND :
The apt value of x and y that satisfies the above condition.



FOR CLARITY :
Refer the Attachment.



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Answer 1

$\large\underline{\sf{Given- }}$

$\rm :\longmapsto\:{ \rm {5 \dfrac{3}{ x} \: \times \: y\dfrac{1}{2}} \: = \: 19}$

$\large\underline{\sf{To\:Find - }}$

The values of x and y

$\large\underline{\sf{Solution-}}$

Given that

$\rm :\longmapsto\:{ \rm {5 \dfrac{3}{ x} \: \times \: y\dfrac{1}{2}} \: = \: 19}$

Let we first convert the mixed fraction to rational form

$\rm :\longmapsto\:{ \rm { \dfrac{5x + 3}{ x} \: \times \: \dfrac{2y + 1}{2}} \: = \: 19}$

$\rm :\longmapsto\:(5x + 3)(2y + 1) = 19 \times 2x$

$\rm :\longmapsto\:(5x + 3)(2y + 1) = 38x$

$\rm :\longmapsto\:(5x + 3)(2y + 1) = 38 \times x$

So, two cases arises,

$\rm :\longmapsto\:5x + 3 = 38 \: \: \: or \: \: \: 5x + 3 = x$

$\rm :\longmapsto\:5x = 38 - 3 \: \: \: or \: \: \: 5x - x = - 3$

$\rm :\longmapsto\:5x = 35 \: \: \: or \: \: \: 4x = - 3$

$\bf\implies \:x = 7 \: \: \: or \: \: \: x = - \dfrac{3}{4} \: \{rejected \}$

So,

$\bf\implies \:5x + 3 = 38$

and

$\bf\implies \:2y + 1 = x$

$\bf\implies \:2y + 1 = 7$

$\bf\implies \:2y = 7 - 1$

$\bf\implies \:2y = 6$

$\bf\implies \:y = 3$

Thus,

The values of x and y, satisfy

$\rm :\longmapsto\:{ \rm {5 \dfrac{3}{ x} \: \times \: y\dfrac{1}{2}} \: = \: 19}$

are

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \large\boxed{ \rm{ x = 7 \: \: \: and \: \: \: y = 3}}$

Justification :-

Consider,

$\rm :\longmapsto\:{ \rm {5 \dfrac{3}{ x} \: \times \: y\dfrac{1}{2}} \: }$

On substituting the value of x and y, we get

$\rm \: = \: \:{ \rm {5 \dfrac{3}{7} \: \times \: 3\dfrac{1}{2}} \: }$

$\rm \: = \: \:{ \rm {\dfrac{35 + 3}{7} \: \times \: \dfrac{6 + 1}{2}} \: }$

$\rm \: = \: \:{ \rm {\dfrac{38}{7} \: \times \: \dfrac{7}{2}} \: }$

$\rm \: = \: \: 19$

Hence, Justified

Answer 2

Answer:

☆Given:-

5 3 × y 1 =19

x 2

☆To find :-

Want to find the values of x and y .

☆Proof:-

Already given that

5 3 × y 1 =19.

x 2

We should convert the equation into mixed fraction to rational form

= 5x+3 × 2y +1 =19

x 2

(5x+3)×(2y+1)= 19 ×2x

(5x+3)×(2y+1)=38x

In this equation we can take two cases will apears

5x+3=38 , 5x+3=x

5x=38-3 , 5x-x=-3

5x=35 , 4x= -3

x=7 , x=-3/4.

We cant can't take the '-' value in equation so,

x=7.

And now,

2y+1=x(x=7)

2y+1=7

2y=7-1

2y=6

y=6/2

y=3

The value of x =7, y=3.

And substituting the value of x and y in equation we get

=5 3 × 3 1

7 2

= 35+3 × 6+1

7 2

=38 × 7

7 2

=19.

Hope it helps u mate.

Thank you.