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pentagon [3]
3 years ago
10

Kaylee and Olivia go to the movie theater and purchase refreshments for their friends.

Mathematics
1 answer:
KatRina [158]3 years ago
3 0

The price of one bag of popcorn is $3.75

Step-by-step explanation:

Let,

x represent the cost of a bag of popcorn

y represent the cost of a drink.

According to given statement;

4x+12y=30      Eqn 1

x+6y=11.25      Eqn 2

Multplying Eqn 2 by 2

2(x+6y=11.25)\\2x+12y=22.50\ \ \ Eqn\ 3

Subtracting Eqn 3 from Eqn 1

(4x+12y)-(2x+12y)=30-22.50\\4x+12y-2x-12y=7.50\\2x=7.50

Dividing both sides by 2

\frac{2x}{2}=\frac{7.50}{2}\\x=3.75

4x+12y=30 and x+6y=11.25 can be used to find the price of one bag of popcorn and the price of one drink.

The price of one bag of popcorn is $3.75

Keywords: linear equation, elimination method

Learn more about elimination method at:

  • brainly.com/question/11821063
  • brainly.com/question/11871074

#LearnwithBrainly

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1. Solve the given linear equations for 'x':
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<h2>----------------------</h2>

2. 3x /4 - 7 /4 = 5x + 12

\frac{3x}{4}  -  \frac{7}{4}  = 5x + 12 \\  \\  \frac{3x}{4}  - 5x = 12 +  \frac{7}{4}  \\  \\  \frac{3x - 20x}{4}  =  \frac{48 + 7}{4}  \\  \\  \frac{ - 17x}{4}  =  \frac{55}{4}

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<h2>-------------------</h2>

3. x +7 - 8x/3 = 17/6 - 5x/8

x + 7 -  \frac{8x}{3}  =  \frac{17}{6}  -  \frac{5x}{8}

put x = 4

4 + 7 -  \frac{ 8\times 4}{3}  =  \frac{17}{6}  -  \frac{5 \times 4}{8}  \\  \\ 11 -  \frac{32}{3}  =  \frac{17}{6}  -  \frac{20}{8}  \\  \\  \frac{33 - 32}{3}  =  \frac{68 - 60}{24}  \\  \\  \frac{1}{3}  =  \frac{8}{24}  \\  \\  \frac{1}{3}  =  \frac{1}{3} .

L.H.S. = R.H.S.

<h2>--------------------</h2>

4. Let 3 consecutive integers : x , x+1 , x+2

As per the question : 2x + 3(x+1) + 4(x+2) = 56

9x + 11 = 56

Transpose 11 to RHS

9x = 45

Divide both sides by 9

x = 5 ,

x + 1 = 5 + 1 = 6

x + 2 = 5 + 2 = 7

Numbers are 5 , 6 and 7 .

<h2>-----------------------</h2>

5. Let the age of Jane’s younger sister is x.

Age of Jane will be x + 6

As per the question, after 10 years the sum of their ages will be 50.

After 10 years,

age of Jane = x + 16

age of her younger sister = x + 10

Therefore,

x + 16 + x +10 = 50

2x + 26 = 50

2x = 24

x = 12

Thus, the present age of Jane’s younger sister is 12 years.

And of Jane’s is 12 + 6 = 18 years.

<h2>---------------------</h2>

6. Let the breadth of rectangular swimming pool be x metres.

Then, its length = (2x + 2) metres.

We know that the Perimeter of a rectangle

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= 2(2x + 2 + x) = 6x + 4

According to the given condition, we have

6x + 4 = 154

6x = 154 − 4

6x = 150

[Dividing both sides by 6]

x = 25

Thus, breadth = 25 m and

length = 25 × 2 + 2 = 52 m .

<h2>---------------------</h2>

7. Let the digit in ten's .

Place be x and the digit in the one's place be y.

x − y = 5 ⟶ (i)

Two digit number = 10x + y

Two digit after reversing the digits = 10y + x

According to question ,

10x + y + 10y + x = 99

11x + 11y = 99

x + y = 9 ⟶ (ii)

On adding (i) and (ii),

2x = 14

x = 7

Putting the value of x in equation (i)

x − y = 5

y = 2

Number = 10x + y

=72 .

<h2>-----------------------</h2>

8. Let the speed of the steamer in still water be x km/h.

Then , the speed downstream = (x+2) km/h

and the speed upstream = (x−2) km/h

Given , distance covered in 4 hours downstream = distance covered in 5 hours upstream

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[Transposing 5x to LHS and 8 to RHS]

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<h2>-----------------------</h2>

9. Let the number of notes of different denomination be x.

∴ Numbers of Rs 100 notes , 50 notes and Rs 10 notes will be 2x , 3x and 5x respectively.

Amount of 100 Rs notes ⇒Rs 100 × 2x = 200x

Amount of 50 Rs notes ⇒Rs 50 × 3x = 150x

Amount of 10 Rs notes ⇒Rs 10 × 5x = 50x

As per the question

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200x + 150x + 50x = 400000

400x = 400000 , x = 1000

No of Rs 100 notes = 2x = 2 × 1000 = 2000

No of Rs 50 notes = 3x = 3 × 1000 = 3000

No of Rs 10 notes = 5x = 5 × 1000 = 5000 .

<h2>------------------------</h2>

10. Let the age of the man be x

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2 years later from now,

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and age of his son will be = (x − 24 + 2) = x − 22

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2(x − 22) = x + 2

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Therefore ,

Present age of man = 46 years

And present age of his son = 46 − 24 = 22 years .

4 0
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