Question

In a zoo, there are ducks and deer. If the total number of heads is 200 and the
the total number of legs are 570, and then find the number of deer.

Answer 1

Step-by-step explanation:

$let \: number \: of \: duck = x \\number \: of \: deer= y \\ Number \: legs \: the \: duck \: have = 2x \\ Number \: legs \: the \: deer \: have = 4y \\ \blue{\mathfrak{\underline{\large{according \: to \: the \: question}}}:} \\ x + y = 200 - (i) \\ 2x + 4y = 570 - (ii) \\ \blue{\mathfrak{\underline{\large{multiply \: equation \: (i) \: by \: 2}}}:} \\ 2x + 2y = 400 - (iii) \\ \blue{\mathfrak{\underline{\large{Subtract \: equation \: (iii) \: in \:(ii)}}}:} \\ 2x + 4y = 570 \\ 2x + 2y = 400 \\ \: \: \: \: \: \: - \: \: \: \: \: \: \: \: \: - \: \: \: \: \: \: \: \: \: \: - \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ - - - - - - - \\ 2y = 170 \\ y = 85 \\ \blue{\mathfrak{\underline{\large{Put \: the \:value \: of \: ‘y’ \: in \: equation \: (i) }}}:} \\ x + 85 = 200 \\ x = 115 \\number \: of \: duck= x = 115 \\ number \: of \: deer= y = 85$

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