Question

Tomorrow, Mrs. Wendel's class will be using toothpicks for a science project. Each student must use at least 9 toothpicks for the project.  Mrs. Wendel knows that there is already a bag of 50 toothpicks in the class storage room. She plans to buy x additional toothpicks this afternoon to make sure her class will have enough. If her class has 30 students, which number sentence represents this situation?

Answer 1

The number sentence for Mrs. Wendel's class needing at least 9 toothpicks per student, with 30 students, and a pre-existing supply of 50 toothpicks is 9 \(\times\) 30 + x \(\geq\) 50. The equation shows that Mrs. Wendel needs to buy enough toothpicks so that when added to the existing 50, there are at least 270 toothpicks for the class.

Step-by-step explanation:

The number sentence that represents the situation where each student must use at least 9 toothpicks for a science project, and Mrs. Wendel's class has 30 students, is 9 \(\times\) 30 + x \(\geq\) 50.

This equation takes into account the minimum number of toothpicks each student needs (9), the total number of students (30), the bag of 50 toothpicks already available, and the unknown quantity of additional toothpicks x that Mrs. Wendel plans to purchase.

To find out how many toothpicks in total are needed, we multiply the number of students by the number of toothpicks per student: 9 \(\times\) 30 = 270 toothpicks. Since there are already 50 toothpicks, Mrs. Wendel needs to make sure that the total number of toothpicks she has after purchasing x more is at least 270. Thus, the equation can be set up as 270 \(\leq\) 50 + x, which simplifies to x \(\geq\) 220.

Answer 2

1) Each student must use at least 9 toothpicks for the project and her class has 30 students, so

at least 9*30 toothpicks are needed.

2) Mrs. Wendel has already 50 toothpicks,

so she needs to buy at least (9*30 - 50).

x ≥ 9*30 - 50