Two families went to Rollercoaster World. The Brown family paid $170 for 3 children and 2 adults. The Rodriguez family paid $360 for 4 children and 6 adults. a) If x is the price of a child's ticket in dollars and y is the price of an adult's ticket in dollars, write a system of equations that models this situation. b) Graph your system of equations on the set of axes below. 80 70 60 50+ 40+ 30- 20- 10- 10 20 30 40 50 60 70 80 Price of Child Tickets (in dollars) Price of Adult Tickets (in dollars) c) State the coordinates of the point of intersection. d) Explain what each coordinate of the point of intersection means in the context of the problem.
Two families went to Rollercoaster World. The Brown family paid $170 for 3 children and 2 adults. The Rodriguez family paid $360 for 4 children and 6 adults. a) If x is the price of a child's ticket in dollars and y is the price of an adult's ticket in dollars, write a system of equations that models this situation. b) Graph your system of equations on the set of axes below. 80 70 60 50+ 40+ 30- 20- 10- 10 20 30 40 50 60 70 80 Price of Child Tickets (in dollars) Price of Adult Tickets (in dollars) c) State the coordinates of the point of intersection. d) Explain what each coordinate of the point of intersection means in the context of the problem.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Rollercoaster World Ticket Pricing Problem
#### Problem Description:
Two families went to Rollercoaster World.
- The Brown family paid $170 for 3 children and 2 adults.
- The Rodriguez family paid $360 for 4 children and 6 adults.
#### Tasks:
**a) System of Equations**
If \(x\) is the price of a child's ticket in dollars and \(y\) is the price of an adult's ticket in dollars, write a system of equations that models this situation.
\[
\begin{cases}
3x + 2y = 170 \\
4x + 6y = 360
\end{cases}
\]
**b) Graphing the System of Equations**
Graph your system of equations on the set of axes below.
**Graph Explanation:**
The graph is a standard Cartesian plane with the x-axis labeled "Price of Child Tickets (in dollars)" ranging from 0 to 80. The y-axis is labeled "Price of Adult Tickets (in dollars)" ranging from 0 to 80. The first equation, when graphed, will be a straight line depicting the relationship between child and adult ticket prices as per the Brown family's cost. Likewise, the second line will represent the Rodriguez family's cost.
**c) Point of Intersection**
State the coordinates of the point of intersection.
**d) Interpretation of the Point of Intersection**
Explain what each coordinate of the point of intersection means in the context of the problem.
---
### Detailed Explanation:
**a) System of Equations:**
Given the problem statement, we form the following equations:
1. For the Brown family: \(3x + 2y = 170\)
2. For the Rodriguez family: \(4x + 6y = 360\)
**b) Graphing the System of Equations:**
To graph these equations, you need to transform them into slope-intercept form if desired, but it is also possible to plot points derived from the equations directly.
For \(3x + 2y = 170\):
- When \(x = 0\), \(2y = 170\) ⇒ \(y = 85\)
- When \(y = 0\), \(3x = 170\) ⇒ \(x \approx 56.67\)
For \(4x + 6y = 360\):
- When \(x = 0\), \(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc6d7e1bc-1d2f-42fa-81d0-df3472853c39%2Fd8961b89-6607-4f5e-8279-c7fbbd3d7f50%2Fr1nndy4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Rollercoaster World Ticket Pricing Problem
#### Problem Description:
Two families went to Rollercoaster World.
- The Brown family paid $170 for 3 children and 2 adults.
- The Rodriguez family paid $360 for 4 children and 6 adults.
#### Tasks:
**a) System of Equations**
If \(x\) is the price of a child's ticket in dollars and \(y\) is the price of an adult's ticket in dollars, write a system of equations that models this situation.
\[
\begin{cases}
3x + 2y = 170 \\
4x + 6y = 360
\end{cases}
\]
**b) Graphing the System of Equations**
Graph your system of equations on the set of axes below.
**Graph Explanation:**
The graph is a standard Cartesian plane with the x-axis labeled "Price of Child Tickets (in dollars)" ranging from 0 to 80. The y-axis is labeled "Price of Adult Tickets (in dollars)" ranging from 0 to 80. The first equation, when graphed, will be a straight line depicting the relationship between child and adult ticket prices as per the Brown family's cost. Likewise, the second line will represent the Rodriguez family's cost.
**c) Point of Intersection**
State the coordinates of the point of intersection.
**d) Interpretation of the Point of Intersection**
Explain what each coordinate of the point of intersection means in the context of the problem.
---
### Detailed Explanation:
**a) System of Equations:**
Given the problem statement, we form the following equations:
1. For the Brown family: \(3x + 2y = 170\)
2. For the Rodriguez family: \(4x + 6y = 360\)
**b) Graphing the System of Equations:**
To graph these equations, you need to transform them into slope-intercept form if desired, but it is also possible to plot points derived from the equations directly.
For \(3x + 2y = 170\):
- When \(x = 0\), \(2y = 170\) ⇒ \(y = 85\)
- When \(y = 0\), \(3x = 170\) ⇒ \(x \approx 56.67\)
For \(4x + 6y = 360\):
- When \(x = 0\), \(
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