Question

Ms. Harris is stocking up on dry-erase markers for the upcoming school year. She used 56 dry-erase markers last year and plans to use at least that many for next year. The number of markers in each box is two more than three times the number of boxes she purchased for this upcoming school year. Which of the following inequalities can be used to determine b, the number of boxes she purchased.

A. 3b2 - 2b ≤ 56
B. 2b2 - 3b ≤ 56
C. 2b2 + 3b ≥ 56
D. 3b2 + 2b ≥ 56

Answer 1

Answer: D. 3b2 + 2b ≥ 56

Explanation:

Here b represents the number of boxes she purchase in upcoming year,

Since, The number of markers in each box = two more than three times the number of boxes she purchased for this upcoming school year.

Thus, the number of markers in each box = 3b + 2

⇒
`\text{The number of markers in b boxes} = b( 3b + 2 ) = 3b^2 + 2b`

According to the question,

The total number of marker in upcoming year ≥ 56

⇒
`3b^2 + 2b\geq 56`

Answer 2

From the root word “at least” we can say that the operator we will use in this case is equal or more than symbol “≥”. From the choices, we have C and D.

It was also stated 2 more than 3 times the number, hence it must be:

D. 3b2 + 2b ≥ 56