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Shkiper50 [21]
2 years ago
15

A farmhouse shelters 16 animals, some are pigs, and some are ducks. Altogether there are 42 legs. How many pigs are there?

Mathematics
1 answer:
zalisa [80]2 years ago
7 0

Answer:

5 pigs

Step-by-step explanation:

A farmhouse shelters 16 animals, some are pigs, and some are ducks. Altogether there are 42 legs. How many pigs are there?

Let us represent:

Number of pigs = x

Number of ducks = y

Our system of equations is given as:

A farmhouse shelters 16 animals, some are pigs, and some are ducks.

x + y = 16...... Equation 1

x = 16 - y

Altogether there are 42 legs.

Ducks have 2 legs(feet) , pigs have 4 legs,

4x + 2y = 42..... Equation 2

We substitute

16 - y for x in Equation 2

Hence:

4(16 - y) + 2y = 42

64 - 4y + 2y = 42

Collect like terms

- 4y + 2y = 42 - 64

-2y =- 22

y = -22/-2

y = 11 ducks

Solving for x.

x = 16 - y

x = 16 - 11

x = 5 pigs

Therefore, we have 5 pigs

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18 points - Qu. If 16 whole numbers factor into 120. You will see how 32 whole numbers factor into 1200 what does the same princ
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Explanation:

<em>Your premise and conclusion are both incorrect</em>.

120 has the prime factorization ...

  120 = 2³ × 3 × 5

The exponents of the prime factors are {3, 1, 1}. The number of divisors of 120 is the product of the increments of these numbers: (3+1)(1+1)(1+1) = 4·2·2 = 16.

120 has 16 natural-number divisors

__

1200 has the same prime factor and two more: 2·5, so the factorization is ...

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These exponents are {4, 1, 2} and the product of their increments is 5·2·3 = 30.

1200 has 30 natural-number divisors.

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When a number is multiplied by 2, its number of natural-number divisors will be (n+1)/n times the previous number of divisors, where n is the increment of the exponent of 2 that is a factor of the original number.

For 120, 2^3 is the power of 2 that is a factor. So, multiplying the number by 2 multiplies the number of divisors by (4+1)/4 = 5/4.

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Likewise, multiplying this number (240) by 5 will multiply its number of divisors by (2+1)/(1+1) = 3/2, where 1 is the power of 5 that is a factor of 240.

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__

<em>Summary</em>

The number of divisors of an integer is the product of the increments of the exponents of its prime factors.

_____

<em>For reference</em>

Here are the divisors of 120:

  1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

Here are the divisors of 240:

  1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240

Here are the divisors of 1200:

  1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200

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Answer:

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Step-by-step explanation:

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