Kayla's school is selling tickets to the annual dance competition. On the first day of ticket sales the school
sold 3 senior citizen tickets and 5 child tickets for a total of $70. The school took in $216 on the second day by
selling 12 senior citizen tickets and 12 child tickets. Find the price of a senior citizen ticket and the price of a
child ticket.

Answers

Answer 1

Answer:

senior ticket = $10     child's ticket = $8

Step-by-step explanation:

s = senior ticket

c = child's ticket

We need to write 2 equations, and we have 2 unknowns, s and c.

3s + 5c = $70

12s + 12c = $216

First solve for s using the first equation.

3s + 5c = 70    Subtract 5c from each side

3s + 5c - 5c = 70 - 5c

3s =  70 - 5c     Divide each side by 3

3s/3 =  (70 - 5c)/3

s = [tex]\frac{70 - 5c}{3}[/tex]

Now plug in s into the second equation.

12s + 12c = 216

12([tex]\frac{70 - 5c}{3}[/tex]) + 12c = 216

[tex]\frac{12}{3}[/tex] (70 - 5c) + 12c = 216

4 (70 - 5c) + 12c = 216

280 - 20c + 12c = 216

280 - 8c = 216  Add 8c to each side

280 - 8c + 8c = 216 + 8c

280 = 216 + 8c   Subtract 216 from each side.

280 - 216 = 216 - 216 + 8c

280 - 216 = 8c

64 = 8c   Divide each side by 8

64/8 = 8c/8

64/8 = c

8 = c

Now plug c into the first equation and solve for s.

3s + 5c = 70

3s + 5(8) = 70

3s + 40 = 70    Subtract 40 from each side.

3s + 40 - 40 = 70 - 40

3s = 70 - 40

3s = 30  Divide each side by 3

3s/3 = 30/3

s = 30/3

s = 10

So a senior ticket costs $10 and a child's ticket costs $8.


Related Questions

PLS HELP!!!
PLS FIND 13 and 15!!

Answers

Answer:

hi how are you doing

Step-by-step explanation:


Determine the equation of the graph with the coordinates of (4, -1)

O y = (x-4)2 - 1
O y=(x + 4)2 + 1
O y = (x + 4)2 - 1
O y = (x - 4)2 + 1

Answers

Answer:

The required equation of the graph with the coordinates of (4, -1) will be:

[tex]y=\left(x-4\right)^2-1[/tex]

The graph is also attached.

Step-by-step explanation:

Given the coordinates (4, -1)

If we put the coordinate values (4, -1) in the given equations, we determine that only [tex]y=\left(x-4\right)^2-1[/tex] is the valid equation as it satisfies the given coordinate value.

For example, putting  (4, -1) in the equation

[tex]y=\left(x-4\right)^2-1[/tex]

[tex]\left(-1\right)=\left(4-4\right)^2-1[/tex]

[tex]-1=\left(0\right)^2-1[/tex]

[tex]-1=0-1[/tex]

[tex]-1=-1[/tex]

So, the equation [tex]y=\left(x-4\right)^2-1[/tex] is true for the coordinate values (4, -1).

Therefore, the required equation of the graph with the coordinates of (4, -1) will be:

[tex]y=\left(x-4\right)^2-1[/tex]

Please check, the graph is also attached.

75 000 in standard form

Answers

Answer:

7.5×10^4

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

Hope this helps <3

Answer: 7.5

Step-by-step explanation:

Is -4(5x)=12 true false or open

Answers

Answer:

False because its -4 if it

Pls help
Simplify the expression: -1.23x + 1.54x + 1.2 + 1.2 + 3.4p

Answers

Answer:

0.31x + 2.4 + 3.4p

Step-by-step explanation:

combine like terms

The answer is 0.31x + 2.4 + 3.4p
You combine like terms

m=-3; (1,4) write in slope intercept form

Answers

Answer:

y = -3x + 7

Step-by-step explanation:

4= -3(1) +0 I’m pretty sure b would be zero because that’s just the y intercept so

PLEASSSSSSSSSSSSSSSSSSSSSSSSSSeeee help 10+ points for you

Answers

Answer:

f < -2

Step-by-step explanation:

f+ 4 < 2

 -4.   -4

f < -2

HOPE THIS HELPS

PLZZ MARK BRAINLIEST

Answer:

the second

Step-by-step explanation:

Solve for x: 81^ x-4=9^3x

Show all work for brainliest

Answers

Answer:

Solve for x by simplifying both sides of the equation, then isolating the variable.x≈−0.00413995,1.6090059

Step-by-step explanation:

Answer:

X=-8

Step-by-step explanation:

81^(x-4)=9^3x

(9^2)^(x-4)=9^3x

9^(2x-8)=9^3x

Same base socompare both sides

So 2x-8=3x

2x-3x=8

-x=8

X=-8

So the value of X is -8

find the slope and y - intercept of the equation.

y=1/4x-8 ​

Answers

slope is 1/4 n y intercept is -8

Answer:

slope= 1/4

y-intercept- (-8)

Step-by-step explanation:

i think i hope this is right !

GIve me an equation then you get 10 points

Answers

Answer:

987654321 divided by 12345678

Step-by-step explanation:

Two metal spheres having volume 50 cm cube and 60 cm cube are melted together to form a new sphere .What is the volume of the new Sphere so formed?​

Answers

Answer:

[tex]110cm^{3}[/tex]

Step-by-step explanation:

[tex]50cm^{3} + 60cm^{3} = 110cm^{3}[/tex]

The volume of an object stays the same no matter how you shape it, so the volume of the new sphere is the sum of the volume of the two metal spheres assuming that nothing is lost during the process of creating the new sphere.

1. Show your work to simplify the expression 0.5(8a +6b) a + 4b​

Answers

Answer:

Using distribute property

0.5(8a)(a) + 0.5(6b)(a) + 4b

4a^2 + 3ab + 4b

Step-by-step explanation:

Answer:

4a+3ab +4b

Step-by-step explanation:

0.5(8a+6b) a +4b

4a +3b*a +4b

4a+3ab +4b

A tennis ball was hit into the air. The height of the tennis ball in feet (h) with respect to how far the ball traveled horizontally in feet (d) can be modeled by the quadratic function,

h = -d2 + 8d+4.

Enter the maximum height, in feet, of the tennis ball.

feet

Answers

Answer:

20m

Step-by-step explanation:

Given the height reached by the ball modelled by the equation

h = -d² + 8d+4.

The velocity of the balk at its maximum height is 0. Hence

v = dh/dd = 0

v = -2d + 8

0 = -2d+8

2d =8

d =8/2

d = 4

Substitute d = 4 into the equation to get the maximum height reached

h = -(4)² + 8(4)+4

h =-16+32+4

h = -16+36

h = 20

Hence the maximum height reached by the ball is 20m

Will give brainiest answer if you are correct​

Answers

Answer:

Well you can either straight up subtract from the total degrees of a triangle using the sum of both of the given angles, which would equal x, or you can make an equation. I’ll do both.

180-78-51=51, x=51

78+51+x=180

129+x=180
x=180-129
x=51

question:

Solve for x: 2/5(x - 4) = 2x

answers:

1/2
-1
1
-8

Answers

Answer:

x= -1

Step-by-step explanation:

plzzzzzzzzzzzz help​

Answers

The answer is 58 square units. I got this answer by dividing the area into 3 parts, the bottom two were both 4 and the big square on top is 50 in total it is 58

Answer:

58

Step-by-step explanation:

Total area = 7 × 10 - 6 × 2 = 70 - 12 = 58 units²

given f(x)=4-3x, what is the value of f(5)?

Answers

Answer:

-11

Step-by-step explanation:

Someone PLease please help me

Answers

Answer is 1 . Righttttttttttttt

If we multiply 0.8 by 1/50, we get 0.8 × 1/50 = 0.8/50 = 0.016 meter. So, we can say 0.016 meter wide should the door be on the scale drawing, if the ratio is 1 to 50.

Answers

Answer:

the ratio is 1:50

this means that 1 meter in the drawing is equal to 50 meters in real life, but that is a complicated way of stating something simple since drawings are not generally measured in meters.

the door is 0.8 meters wide or 80 centimeters wide

in our drawing, the door should be 80 / 50 = 1.6 centimeters wide

the whole purpose of a scale is to allow us to work with smaller units, that is why we have to work with them. It is true that 0.016 meters = 1.6 centimeters, but as I said before, writing the answer in meters just complicates things and makes them harder to understand. You could also say it is 0.000016 kilometers wide and it would be right, but too confusing.

what is the 20th term of the linear sequence?

1,7,13,19,25

Answers

Answer:

115

Step-by-step explanation:

There is a common difference d between consecutive terms, that is

d = 7 - 1 = 13 - 7 = 19 - 13 = 25 - 19 = 6

This indicates the sequence is arithmetic with n th term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 1 and d = 6 , thus

a₂₀ = 1 + (19 × 6) = 1 + 114 = 115

We are required to find the 20th term of the linear sequence.

The 20th term of the linear sequence 1,7,13,19,25 is 115

Given:

1, 7, 13, 19, 25

nth term = a + (n - 1)d

where,

n = number of terms

= 20

a = first term

= 1

d = common difference = 7 - 1

= 6

So,

nth term = a + (n - 1)d

20th term = 1 + (20 - 1)6

= 1 + (19)6

= 1 + 114

= 115

20th term = 115

Therefore, 20th term of the linear sequence 1,7,13,19,25 is 115

Read more:

https://brainly.com/question/17827686

-3/7 + 1/7 please help me i am on a text and i need help

Answers

Answer:

-3/7 + 1/7 equals - 2/7

Step-by-step explanation:

Think of it this way: 3/7- 1/7, then add the negative

Hopefully this helps you!

Answer:

-2 / 7 . Crown?

Step-by-step explanation:

1 / 7  + ( -3 ) / 7 = -2 / 7

Because the positive number is bigger than the negative number on a number line.

Negative numbers are on the left of a number line

Positive numbers are on the right of a number line

If you draw a number line you would go backwards 1 then -3, would become -2 because -2 is greater than -3

Hope this helps.

CAN I also get the crown from your other question and on here too?

someone please please helppp... I need to submit this ttoday..I will mark you the brainliest

Answers

Problem 3

I'm not sure what your teacher is asking here. Identities are equations, but your teacher didn't give you an equation.

=============================================

Problem 4

To show that we have an identity, I'm only going to manipulate the left hand side to transform it into the right hand side. The right hand side will remain the same the entire time.

(3x+7)^2 - 84x = (3x-7)^2

(3x+7)(3x+7) - 84x = (3x-7)^2

(9x^2+21x+21x+49) - 84x = (3x-7)^2

9x^2+42x+49-84x = (3x-7)^2

9x^2-42x+49 = (3x-7)^2

(3x-7)^2 = (3x-7)^2

The two formulas

(a+b)^2 = a^2+2ab+b^2(a-b)^2 = a^2-2ab+b^2

may be handy in terms of expanding out (3x+7)^2 and factoring 9x^2-42x+49

=============================================

Problem 5

x + 1/x = 11

a + b = 11 .... where a = x and b = 1/x

(a+b)^2 = 11^2

a^2 + 2ab + b^2 = 121

x^2 + 2*x*(1/x) + (1/x)^2 = 121

x^2 + 2 + 1/(x^2) = 121

x^2 + 1/(x^2) = 121-2

x^2 + 1/(x^2) = 119

An alternative route is to solve x + 1/x = 11 for x. You'll get two solutions. Use either solution to plug into x^2 + 1/(x^2) to find the result is 119.

posting again since no one would help me :,) PLEASEEEEE I'M STUPID AND NEED HELPPPPPP (plus i'm lazy smh) FREAKING 40 POINTS COME GET IT

Answers

Answer:

ill try to help you

Step-by-step explanation:

1. y=3x+1

2. y= -1.5x+3

3. y=0.5x-3

4. y= 3x

hope this helps

take care

Helpppp!!! Are the triangles below congruent by Side-Side-Side, Side-Angle-Side, or neither?

Answers

Answer

I think it is B or C since there is an angle it can not be A

Step-by-step explanation:

I think it is B since there is 1 angle and 2 sides.

Answer:

C

Step-by-step explanation:

Lets see what we have,

So far we have a side and an angle congruent.

But wait, if two lines intersect, the angle of intersection between the two are equal meaning we have a second angle, and we know now as a result the third angle is 180 minus the two known angles

This means its a Side Angle Angle, however neither of these show this so C

Hope this helps :)

f(x) = -x +2
g(x) = 4.0 – 8

Answers

1) x=1

2) x=-4

hope that helped

Give me the answer for this

Answers

Answer:

>

Step-by-step explanation:

because 16 is greater than 12

Using the Incenter P, find the measure of ∠ZPX.




117°

140°

64°

129°

42°

132°

Answers

Answer:

The measure of ∠ZPX is 63°

Step-by-step explanation:

The given parameters are;

The incenter of the triangle = P

m∠KXP = 31°, m∠PYJ = 27°, [tex]\overline {ZP}[/tex] = 20 feet

Given that the segment [tex]\overline {XJ}[/tex] from the vertex, X, passes through the incenter of the triangle, we have;

The segment [tex]\overline {XJ}[/tex] bisects ∠KXL to form ∠KXP and ∠LXP

Therefore, ∠KXP = ∠LXP = 31°

∠KXL = ∠KXP + ∠LXP = 31° + 31° = 62°

∠KXL = 62°

Similarly;

The segment [tex]\overline {YL}[/tex] bisects ∠KYJ to form ∠PYJ and ∠PYK

Therefore, ∠PYJ = ∠PYK = 27°

∠KYJ = ∠PYJ  + ∠PYK = 27° + 27° = 54°

∠KYJ = 54°

In ΔXYZ, we have, ∠LZJ + ∠KYJ + ∠KXL = 180° based on the sum of the interior angles of a triangle postulate

∴ ∠LZJ = 180° - (∠KYJ + ∠KXL) = 180° - (54° + 62°) = 64°

∠LZJ = 64°

The segment [tex]\overline {ZK}[/tex] bisects ∠LZJ to form ∠PZL and ∠PZJ

Therefore, ∠PZL = ∠PZJ

∠LZJ = ∠PZL + ∠PZJ = 2 × ∠PZL = 64°

∠PZL = 64°/2 = 32° = ∠PZJ

In ΔZPX, we have;

∠PZL + ∠LXP + ∠ZPX = 180° based on the sum of the interior angles of a triangle postulate

∠ZPX = 180° - (∠PZL + ∠LXP) = 180° - (32° + 31°) = 63°

∠ZPX = 63°

The measure of ∠ZPX = 63°

Write the equation in slope-intercept form y−6=−2/5(x−10)

Answers

Answer: y = -2/5x + 10

Step-by-step explanation:

y − 6 = − 2/5 (x − 10)

do distributive property

y - 6 = -2/5x + 4

add six to both sides

y = -2/5x + 10

boom the answer :v

What is the length of the segment DF?

Answers

Let me see the picture of your question. I need to see some angles, side lengths, or ordered pairs for me to answer this question.

Write and solve a word problem that can be modeled by the product 12x-8

Answers

Answer:

Step-by-step explanation:

Mike is at the shop for school supplies. He sees some pencils he wants to buy. He sees that if he buys twelve of the same item, the store will take off $8. How much will twelve pencils cost at the store if one pencil is $5.99?

Equation: 12x-8

12x-8 =

12(5.99) - 8 =

71.88 - 8 =

$63.88

Hope this helps:)

The word problem that can be modeled by the

expression → 12x - 8 is written and solved below.

What is word problem in mathematics?

A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

Given is the following expression -

12x - 8

The world problem is as follows -

An ice cream store sells different flavours of ice cream at different rates. The cost of chocolate flavored ice cream is $12 per piece. If a person buys more than 15 ice - creams and wants it to be packed, the extra cost of packaging is decided by the following formula as →

cost of packaging = c[p] = (n/2) + 2

where n is the cost of ice cream.

If sam buys 'x' ice creams of chocolate flavor for his birthday party, calculate the total amount that sam has to pay to the shopkeeper.

Solution -  

Cost of 1 chocolate flavored ice cream = $12

Cost of x chocolate flavored ice cream = $(12x)

Since, 20 > 15, the extra cost of packing will be -

c[p] = n/2 + 2 = 12/2 + 2 = $8

The equation representing the total cost to be paid is -

Total cost [y] = 12x + 8

y = 12x + 8

Therefore, the word problem that can be modeled by the

expression → 12x - 8 is written and solved above.

To solve more questions on making word problems, visit the link below-

https://brainly.com/question/28756658=

#SPJ2

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