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 and graph the solution on a number line. explain what the solution means in terms of the situation.
Let's first calculate how many minutes it takes to make 400 crochet pieces.
15 minutes/piece * 400 pieces = 6000 minutes
Since there are 60 minutes in an hour, we can convert 6000 minutes to hours:
6000 minutes / 60 minutes/hour = 100 hours
Therefore, it would take 100 hours to make 400 crochet pieces.
Now, we can form the inequality:
Let x be the number of hours spent making crochet pieces.
x ≤ 200
x represents the time in hours, and the inequality states that x should be less than or equal to 200.
To solve the inequality, we graph it on a number line:
|
--------------------------------|------------------------|---------------------------|---->
0 100 200
Since we want x to be less than or equal to 200, we shade the region to the left of 200 on the number line.
The solution in terms of the situation is that the number of hours spent making crochet pieces should be less than or equal to 200. As long as the total time spent making crochet pieces is within this constraint, you will be able to complete the task within the given timeframe.