The Rao family won a raffle of $1,000 to spend at Dixie Amusement Park. They want to use it for a group tour and for meals. A tour can have at most 8 people in the group, and if there are children on the tour there must be at least one adult. The tour cost $250 plus $100 for each adult and $50 for each child. The meal plan for the park is $15 per person.
A) Write a system of inequalities to model this scenario, and graph the system.
B) What is the maximum number of people who could be in the group, and how much would it cost? Justify your answer
C) Suppose that only adults are going to go on the tour. How many can there be? Explain your answer.
Answers
Answer:
Well, 1000>(15x+t)+(50x+100t) if there are children aboard.
B. The maximum amount is 19 if one adult is going with 18 children (not including the meal plan). And the total would be $1000
C. If only adults are going then a total of 8 adults can go if they are planning to use the raffle ticket for the meal plan too. If not then the total is 10.
I hope this is right.
The system of inequalities to model this scenario will be -
x + y ≤ 8
75y + 63x ≤ 200
The common region in the first quadrant gives the possible pair of peoples who can go to the trip.
What is a function? What is equation modelling? What is a mathematical equation and expression?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the functionEquation 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.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Given is that the Rao family won a raffle of $1,000 to spend at Dixie Amusement Park. They want to use it for a group tour and for meals. A tour can have at most 8 people in the group, and if there are children on the tour there must be at least one adult. The tour cost $250 plus $100 for each adult and $50 for each child. The meal plan for the park is $15 per person.
Assume that there are [x] children in the group and [y] adults. So, we can write -
x + y ≤ 8 ... Eq[1]
(250 + 100)y + (250 + 50)x + 15(x + y) ≤ 1000
350y + 300x + 15x + 15y ≤ 1000
375y + 315x ≤ 1000
5(75y + 63x) ≤ 1000
75y + 63x ≤ 200 ... Eq[2]
Refer tot the graph attached. The common region in the first quadrant gives the possible pair of peoples who can go to the trip.
Therefore, the system of inequalities to model this scenario will be -
x + y ≤ 8
75y + 63x ≤ 200
The common region in the first quadrant gives the possible pair of peoples who can go to the trip.
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Related Questions
A prop for a school play is a sphere that will be hung from the ceiling. The surface area of the sphere is 5 024 cm'. If the surface area of the sphere can be found by using the formula SA = 4πr^2. where r is the radius, what is the radius of the sphere, to the nearest cm?
Answers
Answer:
The radius of the sphere, to the nearest cm:
[tex]r\approx 20[/tex] cm
Step-by-step explanation:
The surface area of a sphere is given by the formula
A = 4πr²
where r is the radius of the sphere.
Given
The surface area of sphere A = 5024 cm²The radius of the sphere can be determined such as
[tex]A\:=\:4\pi r^2[/tex]
[tex]r\:=\:\frac{1}{2}\sqrt{\frac{A}{\pi }}[/tex]
Plug in Surface Area of sphere = 5024, π = 3.14 in the formula
[tex]\:r\:=\:\frac{1}{2}\sqrt{\frac{5024}{3.14}}\:\:[/tex]
[tex]r\approx 20[/tex] cm
Therefore, the radius of the sphere, to the nearest cm:
[tex]r\approx 20[/tex] cm
SO 2 chairs are left out. If there are 4781 chairs, find the
The cost of levelling a square lawn at 32 per sq. metre is 3 6272. Find its one side. Also find the cost of
fencing it at 3 per meter.
Answers
Answer:
u need 2321 chairs
Step-by-step explanation:
there u go
this table shows a liner relationship. based on the information in this table. which equation can be used to model the relationship between x and y?
A) y =3x
B) y =85x
C) y = x + 3
D) y = 3x + 255
Answers
i think it is c if its wrong i apologize.
Who is ~Satori Komeiji~ ?
Answers
Answer:
is a character from Touhou Project debuting in the video game, Subterranean Animism. She is the Mistress of the Palace of the Earth Spirits after the underground city was separated from Hell.
Step-by-step explanation:
Answer:
She is the Mistress of the Palace of the Earth Spirits. And in turn is a n anime character
Step-by-step explanation:
Luna Park in Coney Island charges $12 for entry and $2 per ride. Ariana visits the park and goes on 4 rides. How much money did she spend in total?
Answers
2(4) + 12 = 8 + 12 = 20
She spends $20
Solve x^2 — 8x + 15 = 0 by completing the square.
The solutions are x =
and x=
Answers
Completing the square
Therefore x^2 -8x + (8/2)^2 -(8/2)^2+15=0
(X-4)^2 -16+15
(x-4)^2 -1=0
(x-4)^2=1
x-4=+1,-1
x=5 and x=3
Sara had 40 candies. She wanted to give to her friends. She each gave her friends 10 candies each. How many friends does she have??
Answers
[tex]\huge\mathbb\purple{AnSwEr}[/tex]
[tex]\huge❤\bold\red{Hello}❤[/tex]
Hey mate 4 is your Answer
[tex]My \: pleasure \: to \: help \: you \: anytime.[/tex]
[tex]Mark \: me \: as \: brainliest .[/tex]
[tex] \huge \mathscr \pink \star\underline {Follow \: me } \red \star[/tex]
Answer:
4 friends
Step-by-step explanation:
If the roots of a polynomial are 4 and -2 what could the polynomial be
Answers
Answer:
2
Step-by-step explanation:
it may not be right because i guessed
Will give crown help
Answers
Answer:
There are 5 spaces between point J and I
Point J is at (-7,-2)
Point I is at (-2,-2)
They have the same y value, but a difference of 5 in the x value. So, they are 5 units apart.
HELP!!! Plz
You are opening a new business and have to set up utilities. The cable company charges a $49.95 one time connection fee which includes the price of hardware. The cost of the service is $45.95 per month. The phone company charges $79.95 for the connection fee and hardware, plus $29.95 per month. What is the total cost for both services for the first month? _____________ What would be the DIFFERENCE in the cost of the two plans for 12 months? ______________
Blank 1: ____________
Blank 2: _____________
Answers
Answer:
Blank 1: $205.8
Blank 2: $388
Step-by-step explanation:
For blank 1, I added up the 4 numbers because that's what 1 month would cost for both services. For blank 2, I multiplied the monthly fee for each service separately by 12, for 12 months. After that, each equation still separate add the 1 time fee and subtract each company price and you will get your answer.
- I hope this is correct and helpful :)
Phone company costs for a 12-month period are 162 dollars cheaper than cable company costs.
Cable company Connection fee and hardware = 49.95 dollars
Cost of service = 45.95 dollars per month.
Cost for a 12-month period = (connection fee and hardware) + ((cost of service) x 12 months) Cost for a 12-month period = 49.95 dollars + (45.95 dollars per month x 12 months) Cost for a 12-month period = 49.95 dollars + 551.40 dollars Cost for a 12-month period = 601.35 dollars
Phone company Connection fee and hardware = 79.95 dollars Cost of service = 29.95 dollars per month
Cost for a 12-month period = (connection fee and hardware) + ((cost of service) x 12 months) Cost for a 12-month period = 79.95 dollars + (29.95 dollars per month x 12 months) Cost for a 12-month period = 79.95 dollars + 359.40 dollars Cost for a 12-month period = 439.35 dollars Difference in the cost = (cable company cost) - (phone company cost) Difference in the cost = 601.35 dollars - 439.35 dollars Difference in the cost = 162 dollars
Phone company costs for a 12-month period are 162 dollars cheaper than cable company costs.
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shoutout to lester bc i know he's gonna answer this ;) !
Answers
Answer:
A (-3,9)
Step-by-step explanation:
ok easy they they us
R(2,1) and R'(-4,8)
subtract 6 from y and add 7 to y
ok lets solve for S'
S(3,2) now subtract 6 and add 7
(3,2)+(-6,7)
(-3,9)
PLEASE HELP I WILL GIVE GBRAINLIEST
Answers
Find the slope by using 2 sets of x,y values from the table.
Slope is change in y over change in x:
Slope = (-6 - -9) / (1 - -2) = 3/3 = 1
Then the y intercept is the value of y when x is 0. Looking at the table when x is 0 y is -7
The equation would be y = x-7
What is that "break even" cost? *
Answers
Answer:
$61
Step-by-step explanation:
When each company sells 6 shirts, they have $48 (CS) and $45 (TT). When you add their shipping prices, they both have $61.
Dan invests £8200 into his bank account he receives 2% per year compound interest how much will Dan have after 7 years ?
Answers
================================================
Work Shown:
A = P*(1+r/n)^(n*t)
A = 8200*(1+0.02/1)^(1*7)
A = 9419.2224747241
A = 9419.22
Note: I assumed the bank is using annual compounding. The instructions didn't mention it, so that's why I went with n = 1. If your teacher or textbook mention otherwise, say monthly compounding, then you'll change n to n = 12. I would ask for clarification.
A teacher uses 36 centimeters of tape to hang up 9 student projects. At that rate, how much tape would the teacher need to hang up 10 student projects?
Answers
The teacher would need 40 centimeters of tape to hang 10 student projects.
Step-by-step explanation:
Given,
Tape used to hang projects = 36 centimeters
Number of projects hanged = 9
We will find unit rate;
9 projects = 36 centimeters
1 project = \frac{36}{9}\ centimeters
9
36
centimeters
1 project = 4 centimeters
Therefore,
Tape needed to hang 10 projects = 4*10 = 40 centimeters
The teacher would need 40 centimeters of tape to hang 10 student projects.
Keywords: unit rate, multiplication
PLEASEEE HELPM ME I WILL GIVE BRAINLIEST
what is a simile for abortion
Answers
Answer:
abortion is like killing a baby as a mother
Step-by-step explanation:
simile uses "like" or "as"
What is the expression for 7 times the sum of 24 and 36?
Answers
Answer:
7 x (24 + 36)
Step-by-step explanation:
Answer:
7 x (24 + 36)
Step-by-step explanation:
Brainliest?
MULTIPLE CHOICE QUESTION
Evaluate f(x) = 3x - 5, whenx = -1
•f(-1)=8
• f(-1) = -8
•f(-1) = 2
•f(-1) = -2
Answers
what is exponential rate of change
Answers
Answer:
Exponential growth refers to an increase based on a constant multiplicative rate of change over equal increments of time,that is a percent increase of the original amount over time.
What is the value of 7 in 46.897
Answers
Answer:
7 thousandths
Step-by-step explanation:
ez dub
−2, −1, 4 , find all numbers listed that are solution of the equation. (Careful, there might be more than one that work!) If you find several solutions, separate them with a comma. If none of the given numbers work, just enter DNE for 'does not exist'.
k3−k2+k−4=−2k2+k−4
Answers
Answer:
k3-k2+k-4=−2k2+k−4 that is the answer
Jackie wants to purchase a class ring. She found the same ring for $225 at three different stores. The discounts the stores are offering are shown in the table below.
Jewelry Stores
Store Discount
1 25%
2 $25
3 1/3
Which statement about the sales price of the ring is true?
A. Store 1 and Store 2 have the same sales price of $200.
B. Store 3 has the best sales price of $150.
C. Store 1 has the best sales price of $168.75.
D. Store 3 has the best sales price of $75.00.
Answers
Answer:
A
Step-by-step explanation:
im not sure tho
Solve for N!! Please
Answers
Answer:
18
Step-by-step explanation:
[tex]\frac{6}{5} =\frac{N}{15} \\N=\frac{6}{5} \times 15=18[/tex]
In a game of spinning wheels, Ann got to spin a wheel twice. She scored –50 points for the first spin and 90 points for the second spin. If her score at the beginning was zero, then what would be her total score after the two spins?
Answers
Answer:
40
Step-by-step explanation:
-50 + 90 = 40
Q. Of the 100 students in 7th grade , 4 out of every 10 students said that pizza
was their favorite food. Based on this, how many students did NOT say pizza was their
favorite food?
Answers
4:10
To get the total students to 100, you must multiply 10 by 10. Therefore multiply 10x10 and 4x10
This gives a
40:100 ratio
That is how many said pizza is their favorite
To find how many did not, subtract 100-40 (total-part). This gives 60. That means 60 students didn’t say pizza is their favorite.
60
Hope this helps
Which of the following describes a way to graph the function g(x) = -1/2 |x|?
Answers
please help!:)
simplify the complex fraction -9/10 1 3/5
Answers
Answer:
It equals -1 11/25
Step-by-step explanation:
In 2005 the population of a district was 35.700 with a continuous annual growth rate of approximately 4%, what will the population be in 2030 according to the exponential growth function? Round the answer to the nearest whole numberdo not include the unit in your answer.
Answers
Given:
Population is 2005 = 35,700
growth rate = 4% = 0.04
To find:
The population in 2030.
Solution:
The general exponential growth model is
[tex]y=a(1+r)^t[/tex]
where, a is initial value, r is growth rate and t is time in years.
Let the initial year is 2005. So, number of years between 2005 to 2030 is
[tex]2030-2005=25[/tex]
Putting a=35,700, r=0.04 and t=25 in the above model.
[tex]y=35,700(1+0.04)^{25}[/tex]
[tex]y=35,700(1.04)^{25}[/tex]
[tex]y=35,700(2.665836)[/tex]
[tex]y=95170.3452[/tex]
Approximate the value to the nearest whole number.
[tex]y\approx 95,170[/tex]
Therefore, population of the district will be about 95,170.
Amount in 2030 is $95,169
Given that:
Amount invested = $35,700
Growth rate = 4% = 0.04
Time invested = 2030 - 2005
Time invested = 25 year
Find:
Amount in 2030
Computation:
A = P[1+r]ⁿ
Amount in 2030 = 35700[1+0.04]²⁵
Amount in 2030 = 35700[1.04]²⁵
Amount in 2030 = 35700[2.6658]
Amount in 2030 = $95,169
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Se contrató a un arquitecto para construir un monumento conmemorativo. La estructura sería una pirámide formada con balas de cañón. La base sería un cuadrado hecho con 100 balas, la capa siguiente tendría 81 balas y así se continuaría construyendo. La pregunta es, ¿Cuántas balas se utilizaron para construir el monumento?
Answers
Answer:
385 balas de cañon
Step-by-step explanation:
la base mide 10 x 10 = 100 balas de cañon
la capa siguiente mide 9 x 9 = 81 balas de cañon
la siguiente 8 x 8 = 64
despues 7 x 7 = 49
luego 6 x 6 = 36
y seguimos adelante con 5 x 5 = 25, 4 x 4 = 16, 3 x 3 = 9, 2 x 2 = 4 y finalmente tenemos 1 sola bala de cañon.
El total de balas de cañon = 100 + 81 + 64 + 49 + 36 +25 + 16 + 9 + 4 + 1 = 385 balas de cañon
A line passes through the points (2, -4) and (4, 2). What is the equation of this line in slope-intercept form?
Answers
Answer:
A:y=3x-10
Step-by-step explanation: the rise and run is 6/2 and the y intercept is -10