The cost (y), in dollars, to purchase x dozen doughnuts from Bakery A and Bakery B can be found using the equations shown in the table.

Question

 
Bakery Cost ,begin bold,(,end bold,y) A y equals 9 x B y equals 8 x
Question
Choose ,begin emphasis,all,end emphasis, of the statements that are true based on the equations given. 

Answer 1

To analyze the equations given for the cost of purchasing doughnuts from Bakery A and Bakery B, we have:

• For Bakery A: \( y = 9x \)
• For Bakery B: \( y = 8x \)

Here \( y \) represents the total cost in dollars, and \( x \) represents the number of dozen doughnuts purchased.

Let's determine which statements could be true regarding these equations:

1. The cost of doughnuts from Bakery A is more expensive than from Bakery B.

   • This statement is true because for any given \( x \), the cost from Bakery A (\( 9x \)) is always greater than the cost from Bakery B (\( 8x \)), assuming \( x > 0\).

2. If 1 dozen doughnuts is purchased, Bakery B will have a cost of $8.

   • This statement is true because substituting \( x = 1 \) into Bakery B’s equation gives \( y = 8 \cdot 1 = 8 \).

3. If 2 dozen doughnuts are purchased, Bakery A will cost $18.

   • This statement is false. Substituting \( x = 2 \) into Bakery A’s equation gives \( y = 9 \cdot 2 = 18 \), so the statement is actually true.

4. To purchase 0 dozen doughnuts, the cost would be $0 for both bakeries.

   • This statement is true because substituting \( x = 0 \) into either equation gives \( y = 9 \cdot 0 = 0 \) for Bakery A and \( y = 8 \cdot 0 = 0 \) for Bakery B.

5. The cost of purchasing x dozen doughnuts at Bakery A grows at a faster rate than at Bakery B.

   • This is true because the rate of change (slope) for Bakery A (9) is greater than that for Bakery B (8).

In summary, based on these equations, the following statements are true:

• The cost of doughnuts from Bakery A is more expensive than from Bakery B.
• If 1 dozen doughnuts is purchased, Bakery B will have a cost of $8.
• If 2 dozen doughnuts are purchased, Bakery A will cost $18.
• To purchase 0 dozen doughnuts, the cost would be $0 for both bakeries.
• The cost of purchasing x dozen doughnuts at Bakery A grows at a faster rate than at Bakery B.

Feel free to give me a list of specific statements, and I can confirm their validity!