Chris and Bethany are each hosting a lemonade stand. At noon, Bethany challenges Chris to see who can sell the most cups of lemonade that day.

Question

The table shows the total number of cups of lemonade Chris sold at the end of each remaining hour of his sale.

Time (h) Number of cups sold
0 7
1 10
3 16
5 22
The equation y = 4x + 5 shows the number of cups of lemonade Bethany sold for the remaining hours of her sale, with y representing the number of cups sold and x representing the time in hours.

Which statements about the lemonade stands are true?

Select each correct answer.



Responses

Bethany had sold more cups of lemonade than Chris at noon.
Bethany had sold more cups of lemonade than Chris at noon.

Beginning at noon Chris sold 7 cups of lemonade each hour.
Beginning at noon Chris sold 7 cups of lemonade each hour.

Beginning at noon Bethany sold 4 cups of lemonade each hour.
Beginning at noon Bethany sold 4 cups of lemonade each hour.

Chris had sold 7 cups of lemonade when the challenge started at noon.

Answer 1

Let's analyze the given information step-by-step.

Chris's Sales Data

From the data provided, we can calculate how many cups Chris sold each hour:

• At hour 0 (noon): 7 cups sold
• At hour 1: 10 cups sold (an increase of 3 cups from hour 0)
• At hour 3: 16 cups sold (an increase of 6 cups from hour 1)
• At hour 5: 22 cups sold (an increase of 6 cups from hour 3)

From this, we can observe that Chris's sales do not appear to be consistent each hour.

However, since the last cup count at hour 0 is 7, we can deduce:

• Chris sold 7 cups at noon (hour 0).

Bethany's Sales Equation

Bethany’s sales are modeled by the equation \( y = 4x + 5 \), where:

• \( y \) is the number of cups sold,
• \( x \) is the number of hours since noon.

Calculating her sales for each hour:

• At hour 0: \( y = 4(0) + 5 = 5 \) cups
• At hour 1: \( y = 4(1) + 5 = 9 \) cups
• At hour 2: \( y = 4(2) + 5 = 13 \) cups
• At hour 3: \( y = 4(3) + 5 = 17 \) cups
• At hour 4: \( y = 4(4) + 5 = 21 \) cups
• At hour 5: \( y = 4(5) + 5 = 25 \) cups

Analysis of Responses

1. Bethany had sold more cups of lemonade than Chris at noon.

   • False: Bethany sold 5 cups at noon, whereas Chris sold 7 cups. Chris sold more than Bethany at noon.

2. Beginning at noon Chris sold 7 cups of lemonade each hour.

   • False: Chris sold 7 cups at noon but did not sell a consistent 7 cups each hour afterwards.

3. Beginning at noon Bethany sold 4 cups of lemonade each hour.

   • False: According to the equation, Bethany sold 4 additional cups per hour beyond the initial 5; thus, her sales were 4 cups the first hour, then increased thereafter.

4. Chris had sold 7 cups of lemonade when the challenge started at noon.

   • True: At noon (hour 0), Chris had indeed sold 7 cups.

Conclusion

The only true statement from the options provided is: Chris had sold 7 cups of lemonade when the challenge started at noon.