i have 200 hours to make my crochet pieces. i need to make 400 crochet pieces and it takes me 15 minutes to make one crochet piece. what would the inequality that represents my time constraint? then solve the inequality. graph the solution on a number line just in brackets. explain what the solution means in terms of the situation.
Let's denote the total number of crochet pieces as C. We are given that it takes 15 minutes to make one crochet piece, so the total time required to make C crochet pieces can be represented as 15C minutes.
We are also given that you have 200 hours to complete the crochet pieces. Since 1 hour equals 60 minutes, the total time available can be represented as 60 * 200 = 12,000 minutes.
So, the inequality that represents the time constraint is:
15C ≤ 12,000
To solve this inequality, we will divide both sides by 15:
C ≤ 12,000 / 15
C ≤ 800
The solution to the inequality is C ≤ 800. This means that you can make up to 800 crochet pieces within the 200 hours given.
To graph this solution on a number line, we will plot a closed bracket at 800 and shade the area to the left of it, indicating that all the values less than or equal to 800 satisfy the inequality.
|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|
0 100 200 300 400 500 600 700 800 900 1000
The solution on the number line is [800, ∞). This means that in terms of the situation, you can make any number of crochet pieces up to and including 800 within the given time constraint of 200 hours.