Question

=
c) 47 = 10a + 3a + 12
Solve the following linear equations by systematic method and represent the solution graphical
a) -(3x +7) = x + 19
b) -12k + 3k =-18​

Answer 1

Appropriate Question:

The denominator of a rational number is greater than its numerator by 7. If the numerator is increased by 17 and denominator is decreased by 6, the new number formed becomes 2. Find the original number.

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Given: The denominator of a rational number is greater than its numerator by 7.

❒ Let the numerator be x. And, the Denominator be (x + 7).

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$\qquad\quad\boxed{\bf{\mid{\overline{\underline{\bigstar\: According\: to \; the\; Question \: :}}}}\mid}$

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If the numerator is increased by 17 and denominator is decreased by 6, the new number formed becomes 2.

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Therefore,

Numerator, x = (x + 17)

Also,

Denominator, (x + 7 - 6) = (x + 1)

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Now,

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$:\implies\sf \dfrac{\Big(x + 17 \Big) }{\Big(x + 1 \Big)} = 2 \\\\\\:\implies\sf \Big(x + 17 \Big) = 2 \Big(x + 1 \Big) \\\\\\:\implies\sf x + 17 = 2x + 2\\\\\\:\implies\sf 2x - x = 17 - 2\\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 15}}}}}\;\bigstar$

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Hence,

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Numerator, x = 15

And, Denominator, (x + 7) = 15 + 17 = 22

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$\therefore{\underline{\sf{Hence, \: the\; original\; number\;is \; \bf{\dfrac{15}{22}}.}}}$