PLEASEE SHOW WORK AND PLEASEE WRITE NEATLY ### Ticket Pricing Problem**Problem Statement:**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)** 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.The provided graph has a horizontal axis labeled "Price of Child Tickets (in dollars)" ranging from 0 to 80 in increments of 10. The vertical axis is labeled "Price of Adult Tickets (in dollars)" ranging from 0 to 80 in increments of 10. **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.---**Solution Steps:****a)** Forming the system of equations:Let's denote:- $ x $ = price of a child's ticket in dollars,- $ y $ = price of an adult's ticket in dollars.From the information given:- For the Brown family: $ 3x + 2y = $170 $- For the Rodriguez family: $ 4x + 6y = $360 $So, the system of equations is:\[ 3x + 2y = 170 \]\[ 4x + 6y = 360 \]**b)** Graphing the equations:To graph the two equations, we need to find different points that satisfy each equation.For the first equation ($ 3x + 2y = 170 $):- Setting $ x = 0 $: $ 2y = 170 \Rightarrow y = 85 $ (point: (0, 85)).- Setting $ y = 0 $: $ 3x = 170 \Rightarrow x \approx 56.67 $ (point: (56.

The variable denotes price in dollars of child and represents price of adult in dollars. For Brown…

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- 7어 6어 50 40 30- 20- 10 10 20 30 4o 50 60 70 80 Price of Child 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. Price of Adult Tickets (in dollars)

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- 7어 6어 50 40 30- 20- 10 10 20 30 4o 50 60 70 80 Price of Child 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. Price of Adult Tickets (in dollars)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter6: Systems Of Linear Equations And Inequalities

Section6.6: Systems Of Inequalities

Problem 44PFA

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Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

PLEASEE SHOW WORK AND PLEASEE WRITE NEATLY

### Ticket Pricing Problem

**Problem Statement:**
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)** 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.

The provided graph has a horizontal axis labeled "Price of Child Tickets (in dollars)" ranging from 0 to 80 in increments of 10. The vertical axis is labeled "Price of Adult Tickets (in dollars)" ranging from 0 to 80 in increments of 10.

**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.

---

**Solution Steps:**

**a)** Forming the system of equations:
Let's denote:
- $ x $ = price of a child's ticket in dollars,
- $ y $ = price of an adult's ticket in dollars.

From the information given:
- For the Brown family: $ 3x + 2y = $170 $
- For the Rodriguez family: $ 4x + 6y = $360 $

So, the system of equations is:
\[ 3x + 2y = 170 \]
\[ 4x + 6y = 360 \]

**b)** Graphing the equations:
To graph the two equations, we need to find different points that satisfy each equation.

For the first equation ($ 3x + 2y = 170 $):
- Setting $ x = 0 $: $ 2y = 170 \Rightarrow y = 85 $ (point: (0, 85)).
- Setting $ y = 0 $: $ 3x = 170 \Rightarrow x \approx 56.67 $ (point: (56.

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