Question

The total number of lions and peacocks in
a certain zoo is 50. The total number of their
legs is 140. Then find the number of lions and
peacocks in the zoo.​

Answer 1

Answer :

• Number of lions are 20
• Number of peacocks are 30

Given :

• The total number of lions and peacocks in a certain zoo is 50
• The total number of their legs is 140

To find :

• Number of lions and peacocks in the zoo

Solution :

• Let the number of lions be x
• Let the number of peacocks be y

According to question , the total number of lions and peacocks in a certain zoo is 50 so,

》x + y = 50

x + y = 50 .... eq (1)

we know that, lions has four (4) legs and peacocks has (2) legs.

And total number of their legs is 140 then,

》4x + 2y = 140

Now dividing sides by 2 we get,

》2x + y = 70

2x + y = 70 ... eq (2)

Now Subtracting equation (2) from equation (1) we get,

》2x + y = 70 - x + y = 50

》x = 20

Now Substituting the value of x = 20 in equation (1) we get,

》x + y = 50

》20 + y = 50

》y = 50 - 20

》y = 30

Hence

• Number of lions are 20
• Number of peacocks are 30

Answer 2

☯ Let the number of lions in the zoo be ‘x’ and the number of peacocks be ‘y’.

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• According to the first condition, the total number of lions and peacocks is 50.

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$\:\:\:\:\:\:\:$∴ x + y = 50 …(i)

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☆Lion has 4 legs and Peacock has 2 legs.

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• According to the second condition, the total number of their legs is 140.

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$\:\:\:\:\:\:\:$∴ 4x + 2y = 140

Dividing both sides by 2,

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$\:\:\:\:\:\:\:$∴ 2x + y = 70 …(ii)

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☆ Subtracting equation (i) from (ii),

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$\:\:\:\:\dashrightarrow\:\sf{2x\:+\:y\:=\:70\:-\:x\:+\:y\:=\:50}$

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$\:\:\:\:\dashrightarrow\:\sf{x\:=\:20}$

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• Substituting x = 20 in equation (i),

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$\:\:\:\:\dashrightarrow\:\sf{x\:+\:y\:= \:50}$

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$\:\:\:\:\dashrightarrow\:\sf{20\: +\: y \:= \:50}$

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$\:\:\:\:\dashrightarrow\:\sf{y\: = \:50 \:– \:20\: = \:30 }$

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$\:\therefore\:{\underline{\sf{ The\: number \:of \:lions\: and \:peacocks\: in \:the \:zoo\: are \:{\textsf{\textbf{20 \:and \:30\: respectively }}}}}}.$

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