4. A theater has a seating capacity of 900 and charges $2.50 for children, $4 for students, and $5.50 for adults. At a certain screening with full attendance, there were half as many adults as children and students combined. The total money brought in was $3825. How many children, students, and adults attended the show?
Answers
Answer:
We have 3 variables to solve for. We will start by writing two equations in three variables but, with the given information, will eventually have those equations written in 2 variables. The strategy is to set up equations from the given information and solve the equations simultaneously. Let's assign variables...
c= #children total
s= #students total
a= #adults total
c+s+a=900.............Eq1, total attendance, given
4c+6s+8a=5600....Eq2, total receipts, given
a=(1/2)(c+s)
=(1/2)c+(1/2)s.....Eq3, #adults total, given
Let's substitute Eq3 into each Eqs1,2 to get two equations in two variables...
c+s+(½c+½s)=900.........Eq1, substitute for"s"
1.5c+1.5s=900.......combine like terms
3c+3s=1800.....Eq4, multiple equation
by 2 to eliminate fraction
4c+6s+8(½c+½s)=5600...Eq2, substitute for "s"
4c+6s+(4c+4s)=5600...distribute 8
8c+10s=5600...Eq5, combine like terms
Let's solve newly arrived at Eq4,5 simultaneuously...
3c+3s=1800......Eq4
8c+10s=5600......Eq5
-24c-24s=-14400...Eq4 multiplied by (-8)
24c+30s=16800...Eq5 multiplied by 3
------------------------
6s=2400.....add all terms vertically
∴ s=400.......divide both sides by 6
Substitute value back into Eq4, solve for "c"...
3c+3s=1800...Eq4
3c+3(400)=1800...substitute for"s"
3c+1200=1800
3c=600.....subtract 1200, both sides
∴ c=200....divide both sides by 3
Substitute values back into Eq3, solve for "a"...
a=(1/2)(c+s).............Eq3
=(1/2)(200+400)...substitute for "c,s"
=(1/2)(600)
∴ a=300.....................simplify
We now have our three variables solved. Let's substitute those values back into original Eqs1,2 to check against the problem requirements...
c+s+a=900.......Eq1
200+400+300=900....substitute for "c,s,a"
900=900......true, √check
4c+6s+8a=5600.....Eq2
4(200)+6(400)+8(300)=5600...substitute for
"c,s,a"
800+2400+2400=5600...simplify
5600=5600......true, √check
So our calculated values are correct. Always check your solutions and work!
In summary, we have...
200 children, 400 students, and 300 adults in attendance at the theater for the screening.
Step-by-step explanation:
There were total 150 childrens, 450 students and 300 adults.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is a theater that has a seating capacity of 900 and charges $2.50 for children, $4 for students, and $5.50 for adults. At a certain screening with full attendance, there were half as many adults as children and students combined. The total money brought in was $3825.
Assume that there were [x] childrens, [y] students and [z] adults. Then, we can write the equations as -
x + y + (1/2)(x + y) = 900
2.5x + 4y + (5.5)(1/2)(x + y) = 3825
Plot the graph. We will get x = 150 and y = 450.
Then -
z = (1/2)(150 + 450) = (1/2)(600) = 300
Therefore, there were total 150 childrens, 450 students and 300 adults.
To solve more questions on equation modelling, visit the link below-
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Related Questions
Hello guys, plz help me with this question ASAP! Plz show the working, THANK YOU BROTHER
Answers
Answer:
5.5 min
Step-by-step explanation:
At time t=0 you have 72 grams
at time t = 22 min you have 4.5 grams.
Now
4.5/72 = (1/2)^(t/half-life)
and t=22, so
4.5/72 = (1/2)^(22/half-life)
taking log of both sides:
log(4.5/72)=(22/half-life)log(1/2)
solving for half-life gives half-life = 11/2 = 5.5min
Which set of transformations would prove ΔGFE ~ ΔGHI?
Answers
Answer:
The set of transformation would prove ΔEFG ~ ΔGHI is "Reflect ΔGHI
over x = −2, and dilate ΔG′H′I′ by a scale factor of 2 from point G" ⇒
last answer
Step-by-step explanation:
Answer:
the set of transformation would prove ΔEFG ~ ΔGHI is "Reflect ΔGHI
over x = −2, and dilate ΔG′H′I′ by a scale factor of 2 from point G" ⇒
last answer
Step-by-step explanation:
translate to algebraic: Two times rhe sum of x and 3
Answers
The answer is 2(x+3)
hope it helps!
Answer:
2x + 6
Step-by-step explanation:
2(x +3)
2x +6
multiply x by 2=2x
multiply 3×2=6
2x +6
The length of a rectangle is 5 meters greater then the width. The perimeter is 150 meters. What is the width of the rectangle
Answers
answer:
p=2(l+w)
150=2.5+w
150=10w
150/10=w
15=w
The function c(x) = 18x -10 represents the cost in dollars. How many tickets can you buy?
Answers
Note: It seems you may have unintentionally missed writing the complete question. As total cost is missing.
So, I am assuming how many tickets Mr. XYZ can buy if he/she pays 98 dollars.
The solution would still clear your concept though.
Answer:
Please check the explanation.
Step-by-step explanation:
We know that the slope-intercept form of the line equation
y = mx+b
where m is the slope and b is the y-intercept
Given the function
c(x) = 18x -10
comparing with the slope-intercept form of the line equation
rate of change = slope = m = 18c(x) or y represents the costAccording to the function equation,
'x' represents the number of ticketsAssuming the total cost i.e. c(x) = $98
In order to determine the value of x, set c(x) = 98
i.e.
98 = 18x -10
switch sides
18x - 10 = 98
add 10 to both sides
18x - 10 + 10 = 98 + 10
18x = 108
Divide 18 to both sides
18x/18 = 108/18
x = 6
Therefore, if you can buy x = 6 if you pay 98 dollars.
Please answer these 2 questions first to get them right gets brainliest :'(
Answers
Answer:
The first one is y = 8 and the second one is y = 4.
Step-by-step explanation:
You plug the numbers in for x and then solve the equations.
I’ll love you forever if you help me with this ASAP ;)
Answers
Answer:
A, C, E
Step-by-step explanation:
0.6 + 15b + 4 = 25.6
Let's solve the original equation for b.
15b + 4.6 = 25.6
15b = 21
b = 21/15 = 7/5
A.
15b + 4 = 25
15b = 21
b = 21/15 = 7/5
Equivalent
B.
15b + 4 = 25.6
0.6 was subtracted from the left side but not from the right side of the original equation.
Not equivalent
C.
3(0.6 + 15b + 4) = 76.8
Since 76.8 = 3 * 25.6, this equation was obtained by multiplying both sides of the original equation by 3.
Equivalent
D.
15b = 25.6
4.6 was subtracted from the left side of the original equation, but not from the right side.
Not equivalent
E.
15b = 21
b = 21/15 = 7/5
Equivalent
Answer: A, C, E
f(x) = x4 – 522 – 10x3 + 6 + 10x
Answers
4
−
5
4
6
+
1
0
x
x
4
−546+10x
Can someone please help me with this asap ... Please and thank you
Answers
Answer:
Step-by-step explanation:
From the question given in the picture,
a). Since, NR bisects a straight angle ∠MNP,
∠MNR ≅ ∠PNR
m∠MNR + m∠PNR = 180°
2(m∠MNR) = 180°
m∠MNR = 90°
Therefore, ∠MNR and ∠PNR are the right angles.
Since, QN divides ∠MNR in two parts,
Therefore, ∠QNR will be an acute angle (less than 90°).
∠MNR + ∠SNR = ∠MNS
90° + ∠SNR = ∠MNS
Therefore, m∠MNS will be more than 90°.
∠MNS will be an obtuse angle (greater than 90°).
(b). Since, NR divides ∠MNP and ∠QNS,
∠MNR ≅ ∠PNR
∠QNR ≅ ∠SNR
∠MNQ ≅ ∠PNS
(c). m∠MNR = 90°
Since, NR bisects ∠QNS,
∠QNR ≅ ∠RNS
m∠QNR = m∠RNS = 30°
m∠QNR + m∠RNS = 30° + 30°
m∠QNR + m∠RNS = 60°
m∠QNS = 60° [Since, m∠QNS = m∠QNR + m∠RNS]
m∠QNP = m∠QNS + m∠SNP
m∠QNP = m∠QNS + (m∠PNR - m∠SNR)
m∠QNP = 60° + (90° - 30°) = 120°
Please help me happy new years
Answers
1) The quotient is 6.
2) The quotient is 9/10.
Hope it helps!
Answer: 2/4
Step-by-step explanation: You would have to subtract it
write as a product: ac^4-c^4+ac^3-c^3
Answers
I ran out of time and it erased my work. Sorry.
Stephanie is a wedding planner. She has assigned 4 workers for decorating tables with flower bouquets. There are 18 tables at the wedding. If Stephanie increases the number of workers to 8, the tables will be decorated twice as quickly.
Which statement best describes the number of tables in this situation?
A. The number of tables is an independent variable.
B. The number of tables is a dependent variable.
C.The number of tables is neither an independent nor a dependent variable.
D. The number of tables is both an independent and a dependent variable.
Thank you for helping me (:
Answers
Answer:
A
Step-by-step explanation:
Because, you can increase or decrease the number of worker for each table but number of tables will be the same
Answer:
C the person above me is incorrect.
AStep-by-step explanation:
What is
2x + (-2x) + 4 + (-3) in simplified version?
Answers
Or you could simply write 1? Let me know if this helps
i need help with this ?
Answers
Answer:
Range: [-7, 2]
General Formulas and Concepts:
Algebra I
Range is the set of y-values that are outputted by function f(x)Step-by-step explanation:
According to the graph, the line's y-values span from -7 to 2. Since both are closed dot, they are inclusive in the range:
[-7, 2] or -7 ≤ y ≤ 2
Find the circumference of a circle with radius, r = 3.5m.
Give your answer in terms of pi
Answers
Answer:
Find the circumference of a circle with radius, r = 3.5m.
2x3.5xpi = 7pi is answer
1.what is $0.66 as a fraction 2.what is $1.08 as a fraction 3.what is $1.21 as fraction
4.what is $0.52 as a fraction 5.what is $1.71 as fraction 6.what is $0.97 as fraction
Answers
2: 1 8/100
3: 1 21/100
4: 52/100
5: 1 71/100
6: 97/100
1.33/50
2.1 2/25
3.1 21/100
4.13/25
5.1 71/100
6.97/100
David reads 5/8 chapters in 4/5 hours.
What is the unit rate in chapters per hour?
Answers
12x^9y^4/6x^3y^2
A. 2x^3y^2
B. 2/x^6y^2
C. 2/x^3y^2
D. 2x^6y^2
Answers
Answer:b
Step-by-step explanation:
Dylan scored a total of 48 points in the first four games of basketball season which equation can be used to find g e d average number of points he scored per game
Answers
Answer:
[tex]\dfrac{48}{4}=12[/tex]
Step-by-step explanation:
Given that:
Dylan plays basketball.
In the season, he scored 48 points in total in the first four games of the season.
To find:
The equation to represent the average number of points scored per game.
Solution:
Average is the term used to find one number which can be used to represent a list.
It is usually the mid value.
Average can be found by using the following formula:
[tex]\text{Average =} \dfrac{\text{Sum of all the observations}}{\text{Number of observations}}[/tex]
Here, Sum of all the observations is the total score which is given as 48.
Number of observation is nothing but the number of games which is given as 4.
Therefore, the equation to find the average can be written as:
[tex]Average = \dfrac{48}{4}\\ \Rightarrow \bold{Average = 12}[/tex]
A train is accelerating at a rate of 2.0 km/hr squared. If it’s initial velocity is 20 km/hr, what is its velocity after 30 seconds?
Answers
Answer: 30
Step-by-step explanation:
Given the graph below, what is the y-intercept(s)? Give your answer(s) as an ordered pair.
Answers
Answer:
(0, 4)
General Formulas and Concepts:
Algebra I
The y-intercept is the y value when x = 0. Another way to reword that is when the graph crosses the y-axis.Step-by-step explanation:
According to the graph, the line passes the y-axis at y = 4. Therefore, our y-intercept is (0, 4).
Saundra has 8 folders on her computer. Each folder has 50 files. How many files are on Saundra's computer?
Answers
Answer:
400
Step-by-step explanation:
8 x 50 = 400
Answer:
400 files
Step-by-step explanation:
If each folder has 50 files, you would multiply the number of folders by the number of files. So it would be 50 x 8 which equals 400 files.
Jose bought 3 pens and 6 pencils for $6.60. Amy bought 5 pens and 8 pencils for $10.00. How much does one pencil cost?
Appreciate it :)
Answers
Answer:
pen = $1.20, pencil = $0.50
Step-by-step explanation:
let x = pen
let y = pencil
create system of equations:
3x + 6y = 6.60 [can be simplified to be x + 2y = 2.20]
5x + 8y = 10.00
substitution method:
x = 2.2 - 2y
5(2.2 - 2y) + 8y = 10
11 - 10y + 8y = 10
-2y = -1
y = 1/2
solve for 'x':
3x + 6(1/2) = 6.6
3x + 3 = 6.6
3x = 3.6
x = 1.2
what is –9 – (–13) and how do you solve
Answers
A square has a perimeter of 36 millimeters.
What is the area of the square?
Answers
Answer:
A=81
Step-by-step explanation:
Answer:
81
Step-by-step explanation:
36/4=9
9*9=81
main college currently chargea &42000 annually for tuition. to the nearest cent how much will tuition be in 7 years if they raise their tuition by 4% each year?
Answers
Answer:
hii
Step-by-step explanation:
Simplify 3(5a + b) + 4(a + 2b).
A.) 9a + 5b
B.) 19a + 3b
C.) 19a+11b
D.) 9a + 9b
Answers
Answer:
C. 19a + 11b
Step-by-step explanation:
Distribute into the parentheses.
3(5a + b) + 4(a + 2b)
= 15a + 3b + 4a + 8b
Add like terms.
15a + 3b + 4a + 8b
19a + 3b + 8b
= 19a + 11b
Hope that helps.
Hey there!
“Simplify 3(5a + b) + 4(a + 2b)”
FIRST you have to DISTRIBUTE
3(5a + b) + 4(a + 2b)
3(5a) + 3(b) + 4(a) + 4(2b)
3(5a) = 15a
3(b) = 3b
4(a) = 4a
4(2b) = 8b
“15a + 3b + 4a + 8b”
SECOND: COMBINE your LIKE TERMS
(3b + 8b) + (15a + 4a)
(3b + 8b) = 11b ⬅️ BACK number
(15a + 4a) = 19a ⬅️ FRONT number
ALL OF YOUR TERMS/NUMBERS ARE POSITIVE SO WE DON’T HAVE TO FIX ANYTHING
Answer: C. 19a + 11b ☑️
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
A television that costs $500 is marked up 250%. What
is the new price of the television?
Answers
Cost - 500
Marked Up - 250
Margin - 71.4286
MxCxMA= $1,750
This may seem confusing, but its $1,750 for the new price, and the equation is:
M= Marked
C= Cost
MA= Margin
The new price of the television is $1750.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
A television that costs $500 is marked up 250%.
So, the new price is
= 500 + 250% of 500
= 500 + 250/100 x 500
= 500 + 1250
= $1750
Hence, the new price of the television is $1750.
Learn more about Percentage here:
https://brainly.com/question/29306119
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EMERGENCY, EMERGENCY, I WILL GIVE BRAINLIEST
[tex]\frac{1}{4} (2x^{2}-12) = 15[/tex]
Solve for x, do ur steps!!!!!!
Answers
: 1/2x^2-3=15
then you have to add three to both sides so it become
: 1/2x^2=18
then divide by 1/2 to get
:x^2 =36
then take the square root to get a final answer of
:x=6
If a right triangle has a side of length 3 and a hypotenuse of length 9, what is the length of the other side
Answers
Answer:
Step-by-step explanation:
in a right triangle a^2+b^2=c^2,
where a and b are the legs
where c is the hypothenuse
9^2= b^2+3^2
81-9=b^2
b^2=72
b=8.48
Answer:
Step-by-step explanation:
Givens
a = ?
b = 3
c = 9
Formula
a^2 + b^2 = c^2
Solution
a^2 + 3^2 = 9^2
a^2 + 9 = 81
a^2 = 81 - 9
a^2 = 72
Now the tricky part. Are you required to give the exact answer which is
a = √72 = 6√2
or should you give
a = √72 = 8.49