Jenna's parents have given her an interest-free loan of $100 to buy a new pair of running shoes. She plans to pay back the loan with monthly payments of $20 each. a. Write a function rule for the balance function B(p), where p represents the number of payments that Jenna has made. b. After how many payments will Jenna have paid back more than half the loan? Explain your reasoning. c. Suppose the loan amount were $120 and the monthly payments were $15. Write a rule for the new balance function and use it to determine how long it would take Jenna to pay off the loan.

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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## Lesson Performance Task

Jenna's parents have given her an interest-free loan of $100 to buy a new pair of running shoes. She plans to pay back the loan with monthly payments of $20 each.

### Tasks:

a. Write a function rule for the balance function \( B(p) \), where \( p \) represents the number of payments that Jenna has made.

b. After how many payments will Jenna have paid back more than half the loan? Explain your reasoning.

c. Suppose the loan amount were $120 and the monthly payments were $15. Write a rule for the new balance function and use it to determine how long it would take Jenna to pay off the loan.

### Explanation:

There is an accompanying image showing a person trying on a pair of running shoes in a store, potentially indicative of the real-life scenario described in the task.

### Analysis:

This exercise aims to teach students how to create and use linear functions to solve real-life problems involving financial planning and repayment of loans. It provides an opportunity to apply mathematical reasoning to everyday situations.
Transcribed Image Text:## Lesson Performance Task Jenna's parents have given her an interest-free loan of $100 to buy a new pair of running shoes. She plans to pay back the loan with monthly payments of $20 each. ### Tasks: a. Write a function rule for the balance function \( B(p) \), where \( p \) represents the number of payments that Jenna has made. b. After how many payments will Jenna have paid back more than half the loan? Explain your reasoning. c. Suppose the loan amount were $120 and the monthly payments were $15. Write a rule for the new balance function and use it to determine how long it would take Jenna to pay off the loan. ### Explanation: There is an accompanying image showing a person trying on a pair of running shoes in a store, potentially indicative of the real-life scenario described in the task. ### Analysis: This exercise aims to teach students how to create and use linear functions to solve real-life problems involving financial planning and repayment of loans. It provides an opportunity to apply mathematical reasoning to everyday situations.
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