### Problem Analysis and Equation Formation**Scenario Description:**A booster club purchased pizzas for an end-of-season party. They incurred the following costs:- $13 per pepperoni pizza- $11 per plain pizza The total number of pizzas bought was 18, and the total expenditure was $212.**Task:**Form an equation that models the situation described above. Let:- $ x $ represent the number of pepperoni pizzas- $ y $ represent the number of plain pizzas**Step-by-Step Solution:**1. **Identify the costs:** - Cost of one pepperoni pizza ($ x $) = $13 - Cost of one plain pizza ($ y $) = $112. **Set up the equation:** - The number of pepperoni pizzas ($ x $) multiplied by its unit price ($13) plus the number of plain pizzas ($ y $) multiplied by its unit price ($11) should equal the total amount spent ($212).The equation to model this scenario is:\[ 13x + 11y = 212 \]**Drag and Drop Instructions:**Drag and drop the appropriate numbers into the boxes to create the correct equation.\[ \_\_\_\_ x + \_\_\_\_ y = 212 \]**Options Available for Drag and Drop:**- 10- 11- 12- 13- 14- 15***Correct Solution:***\[ 13x + 11y = 212 \]**Graphical Description:**There are no graphs or diagrams in the given text. The instructions revolve around creating an equation to model a given real-world problem regarding the purchase of pizzas.**Educational Notes:**This problem helps students apply algebraic thinking to form and solve equations based on real-life scenarios, reinforcing the concepts of linear equations and cost analysis.

The equation in the form of ax+by=c, with two variables, is considered to be a linear equation,…

- A booster club paid for pizzas for an end of season party. They paid $13 for each pepperoni pizza and $11 for each plain pizza. The club bought a total of 18 pizzas for the party and paid a total of $212. Drag and drop the numbers to the boxes to create an equation which models this situation if x = the number of pepperoni pizzas and y = the %3D number of plain pizzas bought.

- A booster club paid for pizzas for an end of season party. They paid $13 for each pepperoni pizza and $11 for each plain pizza. The club bought a total of 18 pizzas for the party and paid a total of $212. Drag and drop the numbers to the boxes to create an equation which models this situation if x = the number of pepperoni pizzas and y = the %3D number of plain pizzas bought.

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section1.3: Lines

Problem 92E

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Question

### Problem Analysis and Equation Formation

**Scenario Description:**

A booster club purchased pizzas for an end-of-season party. They incurred the following costs:
- $13 per pepperoni pizza
- $11 per plain pizza

The total number of pizzas bought was 18, and the total expenditure was $212.

**Task:**

Form an equation that models the situation described above. Let:
- $ x $ represent the number of pepperoni pizzas
- $ y $ represent the number of plain pizzas

**Step-by-Step Solution:**

1. **Identify the costs:**
- Cost of one pepperoni pizza ($ x $) = $13
- Cost of one plain pizza ($ y $) = $11

2. **Set up the equation:**
- The number of pepperoni pizzas ($ x $) multiplied by its unit price ($13) plus the number of plain pizzas ($ y $) multiplied by its unit price ($11) should equal the total amount spent ($212).

The equation to model this scenario is:
\[ 13x + 11y = 212 \]

**Drag and Drop Instructions:**
Drag and drop the appropriate numbers into the boxes to create the correct equation.

\[ \_\_\_\_ x + \_\_\_\_ y = 212 \]

**Options Available for Drag and Drop:**
- 10
- 11
- 12
- 13
- 14
- 15

***Correct Solution:***
\[ 13x + 11y = 212 \]

**Graphical Description:**
There are no graphs or diagrams in the given text. The instructions revolve around creating an equation to model a given real-world problem regarding the purchase of pizzas.

**Educational Notes:**
This problem helps students apply algebraic thinking to form and solve equations based on real-life scenarios, reinforcing the concepts of linear equations and cost analysis.

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