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yulyashka [42]
2 years ago
7

Tickets for a play cost $3 for children and $10 for adults. A group of 25 people paid a total of $201 for tickets to the play. H

ow many children were in a group?
Mathematics
2 answers:
lidiya [134]2 years ago
8 0

Answer: There were 7 children

Step-by-step explanation:

Let's use <em>x </em>to represent the children and <em>y </em>to represent the adults.

We know they combine to make a group of 25 people so x+y=25

We also know that they paid $201 and that there is $3 per child and $10 for adults so 3x+10y=201

I will solve by substitution.

Solve for y in the first equation

x+y=25\\x-x+y=25-x\\y=25-x

Sub in our value for y into the other equation and solve for x

3x+10y=201\\3x+10(25-x)=201

Step 1) Simplify

3x+250-10x=201\\-7x+250=201

Step 2) Subtract 250 from both sides

-7x+250-250=201-250\\-7x=-49

Step 3) Divide both sides by -7

\frac{-7x}{-7} =\frac{-49}{-7}\\x=7

WITCHER [35]2 years ago
5 0

Answer:

7 children.

Step-by-step explanation:

Let c = children

Let a = adults

1) We can set up two equations and solve them simultaneously using substitution or elimination method.

c + a = 25

3c + 10a = 201

2) I will use substitution. Make one of the variables the subject; then, substitute it into the other equation.

a = 25 - c

3c + 10(25 - c) = 201

3) Solve for c; then, substitute it into one of the equations.

3c + 250 - 10c = 201

-7c = 201 - 250

-7c = -49

c = -49/-7

c = 7

Let's substitute it into one of the equations.

7 + a = 25

a = 25 - 7

a = 18

Since the question only asked for the number of children, the answer is 7.

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Step-by-step explanation:

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Step-by-step explanation:

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The figure shows a cylinder of diameter 12cm and height = 15cm. A hole in the shape of cone is bored into one of its end. If the
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Answer:

\bold{495\pi} \approx \bold{1555.088 cm^3}

Step-by-step explanation:

There was no figure but the question is clear

Volume of a cylinder is given by the formula \bold{\pi r^2h}\\

where r is radius of base of cylinder, h is the height

Volume of a cone is given by \bold{\frac{1}{3} \pi r^2 h}

where r is the radius of base of cone, h is the height

The radius of the cylinder = \frac{1}{2}(diameter) = \frac{1}{2}(12) = 6cm

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Volume of cylinder V_{cyl} = \pi (6)^2  15 = \pi (36)15 = \bold{540\pi}

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Height of cone same as height of cylinder = 15cm

Volume of cone, V_{cone} = \frac{1}{3}\pi r^2 h = \frac{1}{3}\pi (3)^2 15 =  \frac{1}{3}(9)15\pi = \bold{45\pi}\\


Difference is the volume of the remaining solid

V_{cyl} - V_{cone} = 540\pi - 45\pi = \bold{495\pi} \approx \bold{1555.088 cm^3}



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