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solniwko [45]
2 years ago
8

When Katie was visiting her grandpas farm she saw the farm only raised hands and pigs. Katie counted 32 heads and 100 feet in th

e backyard. How many hands and pigs were there in the backyard
Mathematics
1 answer:
QveST [7]2 years ago
8 0

There were 14 hens and 18 pigs in the backyard

Step-by-step explanation:

Katie was visiting her grandpas farm

  • She saw only hens and pigs
  • Katie counted 32 heads and 100 feet in the backyard

We need to find how many hens and pigs in the backyard

Assume that there are x hens and y pigs in the backyard

∵ There are x hens and y pigs in the backyard

∵ There are 32 heads

∴ x + y = 32 ⇒ (1)

∵ Each hen has 2 feet

∵ Each pig has 4 feet

∵ There are 100 feet

∴ 2x + 4y = 100 ⇒ (2)

Let us solve the system of equations to find how many hens and pigs

Multiply equation (1) by -2 to eliminate x

∴ -2x - 2y = -64 ⇒ (3)

- Add equations (2) and (3)

∴ 2y = 36

- Divide both side by 2

∴ y = 18

Substitute the value of y in equation (1) to find the value of x

∵ x + 18 = 32

- Subtract 18 from both sides

∴ x = 14

There were 14 hens and 18 pigs in the backyard

Learn more:

You can learn more about the system of equations in brainly.com/question/2115716

#learnwithBrainly

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<h2>Explanation:</h2>

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