On Saturday, the fruit and juice bar was selling 30 glasses of fruit punch an hour. By 7 p.m., they had sold 270 glasses. If their goal was to sell at least 360 glasses of fruit punch, which inequality can be used to find h, the number of hours they must stay open to make their goal?
a. 270 + 360 > 30h
b. 270 + 30h > 360
c. 270 + 30h < 360
d. 30h < 360 + 270
Let's break down the problem step by step:
Step 1: Determine the number of glasses sold per hour. The fruit and juice bar sold 30 glasses of fruit punch an hour.
Step 2: Calculate the total number of glasses sold by 7 p.m. We are given that they had sold 270 glasses by 7 p.m.
Step 3: Determine the goal number of glasses that the fruit and juice bar wants to sell. The goal is to sell at least 360 glasses.
Now let's determine the inequality that represents the number of hours they must stay open to make their goal.
Step 4: Let h represent the number of hours they must stay open.
Step 5: Calculate the number of glasses sold based on the number of hours they stay open. This can be calculated by multiplying the number of hours (h) by the number of glasses sold per hour (30).
Step 6: Set up the inequality using the information from steps 2, 3, and 5. Since the goal is to sell at least 360 glasses, the inequality should represent this. Therefore, the correct inequality is:
270 + 30h ≥ 360
So the correct answer is option b.
To find the inequality that represents the number of hours the fruit and juice bar must stay open to reach their goal, we need to figure out their current progress and calculate how many more glasses of fruit punch they need to sell.
Given that they are selling 30 glasses of fruit punch per hour and that by 7 p.m. they had already sold 270 glasses, we can calculate the number of hours they have been open as follows:
Number of hours = (Total number of glasses sold) / (Number of glasses sold per hour)
Number of hours = 270 / 30
Number of hours = 9
Therefore, the fruit and juice bar has been open for 9 hours.
Now, let's consider the goal. They want to sell at least 360 glasses of fruit punch. Since they have already sold 270 glasses, they need to sell an additional:
Additional glasses needed = Goal - Total number of glasses sold
Additional glasses needed = 360 - 270
Additional glasses needed = 90
To find the inequality that represents the number of hours they must stay open to reach their goal, we can divide the additional glasses needed by the number of glasses sold per hour:
Number of hours needed = Additional glasses needed / Number of glasses sold per hour
Number of hours needed = 90 / 30
Number of hours needed = 3
Therefore, the inequality that represents the number of hours they must stay open to make their goal is:
30h > 360 - 270
30h > 90
The correct answer is therefore:
b. 270 + 30h > 360