Question

Nick was surveying his field and saw some cows and ducks. Nick counted a total of 80 heads and

Answer 1

Answers:

• Total equation:  x+y = 80
• Legs equation:  2x+4y = 248
• How many ducks? 36
• How many cows? 44

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Further explanation:

• x = number of ducks
• y = number of cows

x+y = 80 is the total equation (ie the head count equation) since we assume each animal has 1 head, and there are 80 heads total.

That equation can be solved to y = 80-x after subtracting x from both sides.

The legs equation is 2x+4y = 248 because...

• 2x = number of legs from all the ducks only
• 4y = number of legs from all the cows only
• 2x+4y = total number of legs from both types of animals combined

We're told there are 248 legs overall, so that's how we ended up with 2x+4y = 248

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Let's plug y = 80-x into the second equation and solve for x.

2x+4y = 248

2x+4( y ) = 248

2x+4( 80-x ) = 248

2x+320-4x = 248

-2x+320 = 248

-2x = 248-320

-2x = -72

x = -72/(-2)

x = 36

There are 36 ducks

Now use this x value to find y

y = 80-x

y = 80-36

y = 44

There are 44 cows.

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Check:

36 ducks + 44 cows = 80 animals total

36*2 + 44*4 = 72 + 176 = 248 legs total

The answers are confirmed.