Question

Theresa volunteers at a food shelf. Today she is filling bags of oranges. When she started, there were 213 oranges. After filling x bags with 3 oranges each, there were fewer than 51 oranges left. How many bags of oranges did Theresa fill?

Part A Write an expression in terms of x for the number of oranges that Theresa bagged.

Part b Write an expression in terms of x for the number of oranges that are left (have yet to be bagged).

Part c Write an inequality using the expression from part B to represent this scenario.

Part d Solve the inequality for the variable x. Use opposite operations on both sides of the inequality until you get x on one side of the inequality by itself.

Part e Did you have to flip the inequality sign? Explain why or why not.

Part f What does the result from part D tell you about Theresa’s situation? Does the answer make sense? Explain.

Part g Think about graphing the inequality you found in part D on a number line. What would it look like?

Choose the correct number:

1. open circle on 54 and arrow pointing right
2.open circle on 54 and arrow pointing left
3.closed circle on 54 and arrow pointing right
4.closed circle on 54 and arrow pointing left

Answer 1

Part A: The number of oranges that Theresa bagged is 3x.

Part B: The number of oranges that are left (have yet to be bagged) is 213 - 3x.

Part C: 213 - 3x < 51

Part D:

213 - 3x < 51

213 - 51 < 3x

162 < 3x

54 < x

Part E: Yes, the inequality sign had to be flipped because we divided both sides by a negative number (-3).

Part F: The result from part D tells us that Theresa filled more than 54 bags of oranges, which makes sense because there were fewer than 51 oranges left.

Part G: The graph of the inequality would be a closed circle on 54 and an arrow pointing to the right. The closed circle indicates that x can equal 54, and the arrow indicates that x can be any number greater than 54.