5. Solve the following problem. You must define your variables, set up a system of equations, and solve algebraically. (Hint: If you're stuck, draw out the table. Perimeter measures the length of the table all the way around) The Rocket Coaster has 15 cars, some that hold 4 people and some that hold 6 people. There is room for 72 people altogether. How many 4-passenger cars are there? How many 6-passenger cars are there?
5. Solve the following problem. You must define your variables, set up a system of equations, and solve algebraically. (Hint: If you're stuck, draw out the table. Perimeter measures the length of the table all the way around) The Rocket Coaster has 15 cars, some that hold 4 people and some that hold 6 people. There is room for 72 people altogether. How many 4-passenger cars are there? How many 6-passenger cars are there?
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Problem 5: Solving a System of Equations
Solve the following problem. You must define your variables, set up a system of equations, and solve algebraically. (Hint: If you’re stuck, draw out the table. Perimeter measures the length of the table all the way around.)
---
**Problem Statement:**
The Rocket Coaster has 15 cars, some that hold 4 people and some that hold 6 people. There is room for 72 people altogether. How many 4-passenger cars are there? How many 6-passenger cars are there?
---
**Solution Approach:**
1. **Define Variables:**
- Let \( x \) be the number of 4-passenger cars.
- Let \( y \) be the number of 6-passenger cars.
2. **Set Up the System of Equations:**
- The total number of cars is 15. Therefore:
\[
x + y = 15
\]
- The total seating capacity is 72 people. Therefore:
\[
4x + 6y = 72
\]
3. **Solve the System Algebraically:**
- **Equation (1):** \( x + y = 15 \)
- **Equation (2):** \( 4x + 6y = 72 \)
- Solve Equation (1) for one variable, for example \( y \):
\[
y = 15 - x
\]
- Substitute \( y \) in Equation (2):
\[
4x + 6(15 - x) = 72
\]
- Simplify and solve for \( x \):
\[
4x + 90 - 6x = 72
\]
\[
-2x + 90 = 72
\]
\[
-2x = 72 - 90
\]
\[
-2x = -18
\]
\[
x = 9
\]
- Substitute \( x = 9 \) back into Equation (1) to solve for \( y \):
\[
9 + y = 15
\]
\[
y = 6
\]
Therefore, there are](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F80a5edf8-1d25-48fa-bf1c-1344aca52412%2Fbb630028-e98e-4968-acfc-8806035f323e%2Ffytan_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem 5: Solving a System of Equations
Solve the following problem. You must define your variables, set up a system of equations, and solve algebraically. (Hint: If you’re stuck, draw out the table. Perimeter measures the length of the table all the way around.)
---
**Problem Statement:**
The Rocket Coaster has 15 cars, some that hold 4 people and some that hold 6 people. There is room for 72 people altogether. How many 4-passenger cars are there? How many 6-passenger cars are there?
---
**Solution Approach:**
1. **Define Variables:**
- Let \( x \) be the number of 4-passenger cars.
- Let \( y \) be the number of 6-passenger cars.
2. **Set Up the System of Equations:**
- The total number of cars is 15. Therefore:
\[
x + y = 15
\]
- The total seating capacity is 72 people. Therefore:
\[
4x + 6y = 72
\]
3. **Solve the System Algebraically:**
- **Equation (1):** \( x + y = 15 \)
- **Equation (2):** \( 4x + 6y = 72 \)
- Solve Equation (1) for one variable, for example \( y \):
\[
y = 15 - x
\]
- Substitute \( y \) in Equation (2):
\[
4x + 6(15 - x) = 72
\]
- Simplify and solve for \( x \):
\[
4x + 90 - 6x = 72
\]
\[
-2x + 90 = 72
\]
\[
-2x = 72 - 90
\]
\[
-2x = -18
\]
\[
x = 9
\]
- Substitute \( x = 9 \) back into Equation (1) to solve for \( y \):
\[
9 + y = 15
\]
\[
y = 6
\]
Therefore, there are
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