Question

Michael is cutting a 100-yard ribbon into pieces 3. 4 yards long. He says that an inequality that represents his project is 3. 4x ≤ 100. Explain what this statement means, in words, and what each part of the inequality represents.

Answer 1

The variable, x, is the number of pieces of ribbon Michael cuts. Since each piece is 3.4 yards long, 3.4x is the total length of all pieces together. This total length cannot be more than 100 yards of ribbon he has, so 3.4x must be less than or equal to 100.

Answer 2

The inequality 3.4x ≤ 100 represents Michael's project of cutting a 100-yard ribbon into pieces that are 3.4 yards long.

In this inequality, x represents the number of pieces of ribbon that Michael needs to cut.

The left-hand side of the inequality, 3.4x, represents the total length of the ribbon after it has been cut into x pieces that are 3.4 yards long.

The inequality says that this total length must be less than or equal to 100 yards, which is the length of the original ribbon.

In other words, Michael can cut the ribbon into x pieces that are 3.4 yards long as long as the total length of the pieces is less than or equal to 100 yards.

If the inequality is true, Michael will have enough ribbon to complete his project. If the inequality is false, he will not have enough ribbon to complete his project.