Question

To make a small vase, Elisa uses no more than 4.5 ounces of clay. To make a large vase, she uses at least 12 ounces of clay. Which compound inequality represents the number of ounces of clay, c, that Elisa uses to make one vase of either size? A. 4.5 < c < 12 B. 4.5 ≤ c ≤ 12 C. c < 4.5 or c > 12 D. c ≤ 4.5 or c ≥ 12

Answer 1

Answer: c ≤ 4.5 or c ≥ 12

Explanation:

Let c denote the number of ounces of clay that Elisa uses to make one vase of either size.

Given statements are: To make a small vase, Elisa uses no more than 4.5 ounces of clay.

The words "no more than" implies "less than or equals to"

hence, for small vase c must be less than or equals to 4.5 oz, which gives

`c\leq4.5`...(1)

To make a large vase, she uses at least 12 ounces of clay.

The word "at least" means "more than or equals to"

hence, for large vase c must be more than or equals to 12 oz, which gives

`c\geq12`...(2)

Combining (1) and (2), we get

c ≤ 4.5 or c ≥ 12

Answer 2

Let c be the ounces of clay that Elisa used. For small vases, the value of c should be less than or equal to 4.5 which can mathematically be expressed as c ≤ 4.5. For large vases, the value of c should be greater than or equal to 12, c ≥ 12. Thus, the answer to this item is letter D.