Question

Jack and Jill were catching tadpoles. At first Jill caught nine times three more than Jack caught. Jack was upset and released half of Jill’s tadpoles, and then six times as many as Jack caught swam away. After all of this, Jill only had three tadpoles left. How many tadpoles did Jack catch?

Answer 1

There are 7 tadpoles which Jack can catch

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Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

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$\green{\underline \bold{\tt{Given :-}}}$

• Jill caught nine times three more than Jack

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• Half of Jill's tadpole were released

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• Six times as many as Jack caught swam away

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• At last Jill was left with three tadpoles

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$\red{\underline \bold{\tt{To \: Find :-}}}$

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• Number of tadpole Jack caught

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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Let the number of tadpole Jack got be "x"

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$\purple{\underline \bold{According \: to \: the \ question :}}$

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$\underline{\bold{\texttt{1st case :}}}$

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• Jill caught nine times three more than Jack

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⭕ Jill got = 9(x + 3)

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$\underline{\bold{\texttt{2nd case :}}}$

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• Half of Jill's tadpole were released

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⭕ Jill left with = $\sf \dfrac { 9(x + 3) } { 2 }$

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$\underline{\bold{\texttt{3rd case :}}}$

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• Six times as many as Jack caught swam away

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⭕ At last jill got = $\sf \dfrac { 9(x + 3) } { 2 } - 6x$

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But at last Jill was left with 3 tadpoles $</strong><strong>\: </strong><strong>\: </strong><strong>\: </strong><strong>\: </strong><strong>$ [ Given ]

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So,

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$\sf \longmapsto 3 = \dfrac { 9(x + 3) } { 2 } - 6x$

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$\sf \longmapsto 3 = \dfrac { 9x + 27 } { 2 } - 6x$

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$\sf \longmapsto 3 = \dfrac { 9x + 27 - 12x } { 2 }$

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$\sf \longmapsto 6 = 9x + 27 - 12x$

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$\sf \longmapsto 6 = -3x + 27$

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$\sf \longmapsto 3x = 27 - 6$

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$\sf \longmapsto 3x = 21$

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$\sf \longmapsto x = \dfrac { 21 } { 3 }$

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$\bf \dashrightarrow x = 7$

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• Hence Jack got 7 tadpoles