AbdurRakib wrote:
A clothing manufacturer makes jackets that are wool or cotton or a combination of wool and cotton. The manufacturer has 3,000 pounds of wool and 2,000 pounds of cotton on hand. Is this enough wool and cotton to make at least 1,000 jackets?
1) Each wool jacket requires 4 pounds of wool, and no cotton
2) Each cotton jacket requires 6 pounds of cotton, and no wool
We are given that a clothing manufacturer makes jackets that are wool or cotton or a combination of wool and cotton, and that the manufacturer has 3,000 pounds of wool and 2,000 pounds of cotton on hand. We need to determine whether there is enough cotton and wool to produce 1,000 jackets.
Statement One Alone:Each wool jacket requires 4 pounds of wool, and no cotton.
Since 3000/4 = 750, this means the manufacturer can make 750 wool-only jackets. However, since we do not know how much cotton is needed to produce a cotton jacket, we do not have enough information to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:Each cotton jacket requires 6 pounds of cotton, and no wool.
Since 2000/6 = 333⅓, the manufacturer can make 333 cotton-only jackets. However, since we do not know how much wool is needed to produce a wool jacket, we do not have enough information to answer the question. We can eliminate answer choice B.
Statements One and Two Together:From statements one and two, we know that each wool jacket requires 4 pounds of wool and no cotton, and that each cotton jacket requires 6 pounds of cotton and no wool.
From the analysis of each statement, we know that the manufacturer can make a maximum of 750 wool jackets and 333 cotton jackets. Since we have enough cotton and wool to produce 750 + 333 = 1,083 jackets, we have enough cotton and wool to produce at least 1,000 jackets.
Answer: C
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