Question

Instructions

Sarah’s neighbor offers to pay her $5 for every shark tooth she finds on the beach. After collecting only three shark’s teeth, Sarah decides to share the opportunity with her friend John. Sarah can find shark teeth twice as fast as John, but she can earn even more money with his help.

Sarah can use the expression 5(2j + 3 + j) to represent the amount of money she can earn.

Part 1: Writing Expressions
Write an expression that looks like Sarah’s expression: 5(2j + 3 + j). Replace the coefficients so that your expression is not equivalent. You may use any number that you choose to replace the coefficients. Be sure to leave the variables the same. For example, 8(3j + 7 + 3j) looks like Sarah’s expression but is not equivalent.


Translate the algebraic expression you created in Question 1 to a verbal expression.


Part 2: Writing Equivalent Expressions
You will now use mathematical properties to create two expressions that are equivalent to the expression you created in Question 1. Make sure you show all steps in your work.



Use either the commutative property or combine like terms to create an equivalent expression.



Use the distributive property to create an equivalent expression.


Pick a number from 1 to 10. Use that number to verify your three expressions (the original, the one from 3a, and the one from 3b) are equivalent by substituting it into each expression. Show all your work for complete credit.




Part 3: Finish the Story
Write a few sentences to end Sarah’s story. How many shark teeth did she find? How many shark teeth did John find? How much money did Sarah earn?
Choose a method to present your assignment. You may submit your work in a Word Document or you may choose to develop a PowerPoint presentation or video recording of yourself. Use your creativity! Make sure to include the information from all three parts in your Word Document or presentation

Answer 1

1.9( j + 8 + j)

2. 9(4 j) + 9 (8 + j)

2. 45 j + 72

Explanation:

1.nine times, open parentheses four times j plus eight plus j

2. 9(5 j + 8)=

Sarah had a total amount of 45 teeth meaning that her neighbor gave Sarah $225.