A skating rink changes one admission price for adults and a different admission price for children. The total admission price for a group of 4 adults and 10 children is $57. The total admission price for a group of 3 adults and 7 children is $41. What are the admission prices for an adult and for a adult?

Answers

Answer 1

Given:

The total admission price for a group of 4 adults and 10 children is $57.

The total admission price for a group of 3 adults and 7 children is $41.

To find:

The admission prices for an adult and for a children.

Solution:

Let the price of an adult be x and price of children be y.

According to the question,

[tex]4x+10y=57[/tex]         ...(i)

[tex]3x+7y=41[/tex]      ...(ii)

Multiply equation (i) by 3.

[tex]12x+30y=171[/tex]         ...(iii)

Multiply equation (i) by 4.

[tex]12x+28y=164[/tex]      ...(iv)

Subtract (iv) from (iii).

[tex]12x+30y-12x-28y=171-164[/tex]

[tex]2y=7[/tex]

Divide both sides by 2.

[tex]y=3.5[/tex]

Put y=3.5 in (i).

[tex]4x+10(3.5)=57[/tex]

[tex]4x+35=57[/tex]

[tex]4x=57-35[/tex]

[tex]4x=22[/tex]

Divide both sides by 4.

[tex]x=5.5[/tex]

Therefore, the price for an adult is $5.5 and price for a child is $3.5.


Related Questions

Solve the inequality Graph the solution set 7 + 4k ≥ 23

Answers

Answer: k ≥ 4

Step-by-step explanation:

7 + 4k ≥ 23

subtract 7 on both sides

4k ≥ 16

divide by 4 on both sides

k ≥ 4

the graph:

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113% I think check with your teacher

Find slop for each line
8x-4y=16

Answers

Use Cymath, it shows you the steps on how to get the slope.

Answer:

y=2x-4

Step-by-step explanation:

slope=mx+b

8x-4y=16

-4y=-8x+16

-4y/-4=y

(-8x+16)/-4=2x-4

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Original price: $80; Markdown: 36%

Answers

Answer:

$51.20

Step-by-step explanation:

36% of 80 is 28.8

80 - 28.8 = 51.2

Formatted properly, the answer is $51.20

Answer:

$51.20

Step-by-step explanation:

The answer is $51.20!

Hope this helps!

Find the slope of the line through the points (-9, 19) and (-13, 11).

Answers

Answer:

slope is 2

Step-by-step explanation:

slope is m= y2-y1/x2-x1= 19-11/-9+13= 8/4=2

16. An airplane 30,000 feet above the ground begins descending at a rate of 2,000 feet per minute. Write an equation to model the situation. Find the altitude of the plane after 5 minutes​

Answers

Answer:

equation: y=-2,000x+30,000

altitude after five minutes: 20,000

Step-by-step explanation:

y = altitude of the plane

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The price of a skateboard was reduced from $150 to $90. By what percentage was the price of the skateboard reduced?​

Answers

Answer:

40%

Step-by-step explanation:

Ignore the zeros, then think about the 15 ‘s multiplication table. Once you do, you will find that 90 is 15 times 6, which is 60%. And 100-60 is obviously 40. Hope this helps.

The percentage that was reduced from the original price is 40 %

What is Percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

Given data ,

The original price of the skateboard = $ 150

The reduced price of the skateboard = $ 90

The difference between the original price and reduced price =
Original price of the skateboard - Reduced price of the skateboard

The difference between the original price and reduced price = 150 - 90

                                                                                                      = $ 60

Let the percentage decrease be A

Now the equation will be

Original price of the skateboard - A % ( Original price of the skateboard ) =
Reduced price of the skateboard

So ,

150 - A/100 ( 150 ) = 90

Adding A/100 ( 150 ) on both sides , we get

A/100 ( 150 ) + 90 = 150

Subtracting 90 on both sides , we get

A/100 ( 150 ) = 60

Multiply by 100 on both sides , we get

150A = 6000

Divide by 150 on both sides , we get

A = 40 %

Hence , the percentage at which the price of the skateboard reduced is 40%

To learn more about percentage click :

https://brainly.com/question/12861068

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write a statement that indicates that the triangles in each pair are congruent

Answers

Number 1 is congruent

Select all of the statements that are true for the given parabola.

Answers

Answer:

A and B are true

Step-by-step explanation:

The minimum is the turning point on the graph and occurs at (1, - 2)

The x- intercepts are where the graph crosses the x- axis , that is at

x = - 1 and x = 3 or in coordinate form (- 1, 0 ) and (3, 0 )

The equation of the axis of symmetry is a vertical line passing through (1, - 2)

with equation x = 1

The true statements are A and B

Answer:

⇨ A and B choice

Step-by-step explanation:

⟺ Consider all choices.

⥱ Choice A is correct because It's upward Parabola ( a > 0) where there is only the minimum point/value. The minimum point is at (1,-2). The vertex for upward parabola can be called the minimum point.

⥱ Choice B is correct because the Parabola intercepts x-axis at (-1,0) and (3,0) from the graph.

⥱ Choice C is wrong because the Axis of Symmetry is supposed to be x-term/value for the Parabola. If it is the y-value/term then it would be Side Parabola.

⥱ Choice D is wrong because an upward Parabola doesn't have the maximum point. The only Parabola with maximum point is downward Parabola ( a < 0)



A bakery made 140 buns. A restaurant bought 80 of the buns. The remaining buns were put into bags of 4 buns each. How many bags of buns
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Answers

Answer:

A bakery made 140 buns. A restaurant bought 80 of the buns. The remaining buns were put into bags of 4 buns each. How many bags of buns

are there?

Answer:

30, 30 bags of buns your welcome

A sum of money is to be divided among Paul, John And Mary in the ratio 2:3:7 respectively. If Mary received $350 more than John. Determine to the nearest whole number, the total sum of money that was shared.

Answers

Answer:

$1050

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1050 is the correct answer your welcome have a nice day !

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Answers

Answer:

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Step-by-step explanation:

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*
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Answers

Answer:

A

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Answers

Answer:

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Step-by-step explanation:

ez dub

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Answers

Answer:

100

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Answer:

ANS 100

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Step-by-step explanation:

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question 16

If y is parallel to z then the given angles are alternate exterior and has same measurement

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Answer:

The solution of the given equation is not possible. Because different variables never multiply or divide

Draw the given​ figure's reflection image across line l. (look at the screenshot)

A.
B.
C.
D.

Answers

Answer:

B

Step-by-step explanation:

B is the right answer

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Answers

Answer:

b

Step-by-step explanation:

Answer:

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Step-by-step explanation:

B.

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Answers

Answer:

Goran's gas tank is 1/6 full. After he buys 14 gallons of gas, it is 3/4 full. How many gallons can Goran's tank hold?"

Let x = gallons to fill the tank

14

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3(3x) = 2x + 168

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see if that is true

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

84

Step-by-step explanation:

Let the number be x.

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LCM(3,4)=12

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Percy has already walked 25 kilometers this week, plus he plans to walk 5 kilometers during
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Answers

Answer:

85

Step-by-step explanation:

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Can you write 10 2/3 as an improper fraction?

Answers

Answer:

10 2/3 is 32/3

Step-by-step explanation:

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.

Step-by-step explanation:

10 2/3

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Answers

Answer:

x=7

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A density curve for all the possible temperatures between 0 degrees F and 40 degrees F is a rectangle. What is the height of the rectangle in this density curve?
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Answers

Answer:

Concept: Higher Level Mathematics

You have a density curve, aka probability You are asked to find the height Hence 0-40F has 40 total integers or values of X(probability) Hence you have a total Area of [tex] \binom{40}{0} [/tex]Integrate f(x) to get 0.025. Hence the answer is A Rate positively and give brainlist

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Answers

Y = 2x + 12
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Answer:

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Step-by-step explanation:

HELP FAST !!! WILL GIVE BRAINLIEST!!

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Answer:

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Step-by-step explanation:

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Answers

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B

Step-by-step explanation:

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