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o-na [289]
3 years ago
9

A farmer was asked how many cows and chickens she has. The farmer replied, "between the cows and the chickens, there are 162 eye

s and 270 feet." How many cows does she have? How many chickens does she have? (Note: chickens have 2 feet and cows have 4 feet.)
Mathematics
1 answer:
Kazeer [188]3 years ago
8 0
<h2>☀️ <u>Solution</u><u>:</u></h2>

We all know that,

  • All animals have 2 eyes.
  • All cows have 4 feet
  • All hens have 2 feet

So, Let the no. of cows be x and chickens be y

According to question,

  • Total number of eyes = 162

Framing equation,

⇛ Eyes of cows + Eyes of chickens = 162

⇛ 2x + 2y = 162

⇛ 2(x + y) = 162

⇛ x + y = 162/2 = 81 -----------(1)

According to question(Cond.-1)

  • Total number of feet = 270

Framing equation,

⇛ Feet of cows + Feet of chickens = 270

⇛ 4x + 2y = 270

⇛ 2(2x + y) = 270

⇛ 2x + y = 135 ----------(2)

Subtracting eq.(1) from eq.(2),

⇛ 2x + y - (x + y) = 135 - 81

⇛ 2x + y - x - y = 54

⇛ x = 54

Putting value of x in eq.(1),

⇛ 54 + y = 81

⇛ y = 81 - 54

⇛ y = 27

⚘ So, Total number of animals,

  • Number of cows = x = 54
  • Number of chickens = y = 27

Hence, solved !!

<u>━━━━━━━━━━━━━━━━━━━━</u>

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QUESTION:

Simplify each expression

ANSWER:

1.) \green{{- 8n}}

2.) \green{{- 2b - 60}}

3.) \green{{- 10x - 14}}

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STEP-BY-STEP EXPLANATION:

1.) First, If the term doesn't have a coefficients, it is considered that the coefficients is 1

WHY?

Learn why:

Why is it considered that the coefficient is 1?

Remember that any term multiplied by \blue{{1}} remains the same :

\blue{{1}} {× x = x}

Step 1:

The equality can be read in the other way as a well, so any term can be written as a product of \blue{{1}} and itself:

{x = } \blue{{1}} {× x}

Step 2:

Usually, we don't need to write multiplacation sign between the coefficient and variable, so the simple form is:

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This is why we can write the term without the coefficient as a term with coefficient {1}

Now let's go back to solving as what i said if a term doesn't have a coefficient, it is considered that the coefficient is 1

{n - 9n}

\red{{1}} {n -9n}

Second, Collect like terms by subtracting their coefficients

\red{{1n - 9n}}

\red{{( 1 - 9)n}}

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how?

Keep the sign of the number with the larger absolute value and subtract the smaller absolute value from larger

\red{{1 - 9}}

\red{{- (9 - 1)}}

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how?

Multiply each term in the parentheses by - 6

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\red{{- 6b - 6 × 10}}

Multiply the numbers

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Second, Collect like term

how?

Collect like terms by calculating the sum or difference of their coefficient

\red{{- 6b + 4b}}

\red{{(- 6 + 4)b}}

Calculate the sum

\red{{(- 6 + 4)}}b

\red{{-2}}b

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3.) First, Distribute 2 through parentheses

how?

Multiply each term in the parentheses by 2

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\red{{2x - 2 × 5}}

Multiply the numbers

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how?

Multiply each term in the parentheses by - 4

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Calculate the product

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how?

Collect like terms by subtracting their coefficient

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\red{{(2 - 12)x}}

Calculate the difference

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how?

Factor out the negative sign from the expression

\red{{- 10 - 4}}

\red{{- (10 + 4)}}

Add the numbers

- (\red{{10 + 4}})

- \red{{14}}

\green{\boxed{- 10x - 14}}

That's all I know sorry but I hope it helps :)

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Read 2 more answers
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