How many of each animal are there, and how do I work it out?: Penguins 2 legs; huskies 4 legs; 200 legs and 72 heads.

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pohnpei397's profile pic

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted on

There are 44 parrots and 28 huskies.  Here is how to get this answer:

We can set up two equations with the information you have given us (assuming both birds and dogs have one head each).

Let H be the number of huskies and P be the number of parrots.  Then we can say

H + P = 72

And we can also say that

4h + 2p = 200

We can say this because the number of huskies (times 4) plus the number of parrots (times 2) will give us 200 legs.

Now let's use the first equation to find a value for H.  We can say that

H = 72 - P

Now we substitute that value into the second equation and we get

4 (72 - P) + 2p = 200

288 - 4p + 2p = 200

288 - 2p = 200

-2p = -88

p = 44

So there are 44 parrots.  If there are 44 parrots then there are 72-44 = 28 huskies.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

If we'll note the number of penguins by a and the number of huskies by b, we'll get:

a+b = 72 (1)

We also could express the number of penguins and huskies, depending on the number of legs:

2a + 4b = 200 (2)

Now, all we have to do is to solve the simultaneous equations (1) and (2).

We'll solve the system using elimination method. For this reason, we'll multiply (1) by -2.

 -2(a+b) = -2*72

-2a - 2b = -144 (3)

We'll add (3) to (2) and we'll get:

-2a - 2b + 2a + 4b = -144 + 200

We'll eliminate like terms:

2b = 56

We'll divide by 2:

b = 28

We'll substitute b in (1):

a+b = 72

a + 28 = 72

We'll subtract 28 both sides:

a = 72-28

a = 44

So, we'll get 44 penguins and 28 huskies.

william1941's profile pic

william1941 | College Teacher | (Level 3) Valedictorian

Posted on

Let the number of penguins be P and the number of huskies be H.

As penguins have 2 legs and huskies have 4 legs, the total number of legs is 2P+ 4H, which is equal to 200.

Both of them have only one head, therefore P+H= 72.

Now solving:2P+ 4H = 200 and P+ H= 72 for P and H we get,

2P+ 4H =200

=> P + 2H = 100

substitute P = 72 - H from P+H= 72.

=> 72 - H + 2H = 100

=> H= 100- 72= 28

And P= 72 - H= 72- 28 = 44

So the number of penguins is 44 and number of huskies is 28

 

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

Let P an H be the number of pengwins and huskies.

So the number of heads:

 = P+H = 72 ............(1)as given.

The number of legs = 2P for penguins and 4H for Huskies. So the total legs:

2P+4H = 200. Or dividing by2, we get:

P+2H = 100..........(2)

 

Eq(2) - eq(1) gives:

P+2H - (P+H) = 100-72. = 28

H = 28.

P = 72-H = 72 - 28  = 44.

Tally = 2P+4H = 44*2+28*4 = 88+112 = 200

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