To evaluate the statements based on the cost equations for both bakeries, we need to determine the cost per doughnut for each bakery.
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Bakery A’s cost equation:
\(y = 9x\)
This means the cost for \(x\) dozen doughnuts is \(9\) dollars per dozen. Since there are \(12\) doughnuts in a dozen, the cost per doughnut for Bakery A is: \[ \text{Cost per doughnut at Bakery A} = \frac{9 \text{ dollars}}{12 \text{ doughnuts}} = \frac{9}{12} = 0.75 \text{ dollars or } 75 \text{ cents} \] -
Bakery B’s cost equation:
\(y = 8x\)
This means the cost for \(x\) dozen doughnuts is \(8\) dollars per dozen. The cost per doughnut for Bakery B is: \[ \text{Cost per doughnut at Bakery B} = \frac{8 \text{ dollars}}{12 \text{ doughnuts}} = \frac{8}{12} = \frac{2}{3} \text{ dollars or } 66.67 \text{ cents} \]
Now, let's examine each statement:
A. Bakery A charges about 8 cents more per doughnut than Bakery B.
- Cost per doughnut at Bakery A: \(75\) cents
- Cost per doughnut at Bakery B: \(66.67\) cents
- Difference: \(75 - 66.67 = 8.33\) cents
- True.
B. The cost of 2 dozen doughnuts is $2 more at Bakery A than Bakery B.
- Cost for 2 dozen at Bakery A: \(y = 9(2) = 18\) dollars
- Cost for 2 dozen at Bakery B: \(y = 8(2) = 16\) dollars
- Difference: \(18 - 16 = 2\) dollars
- True.
C. Bakery A charges $1.33 per doughnut and Bakery B charges $1.50 per doughnut.
- We calculated that Bakery A charges \(0.75\) (or \(75\) cents) per doughnut and Bakery B charges \(0.67\) (or \(66.67\) cents) per doughnut.
- Both values are incorrect.
- False.
D. Bakery A charges $0.75 per doughnut and Bakery B charges $0.67 per doughnut.
- We calculated that Bakery A charges \(0.75\) (or \(75\) cents) per doughnut and Bakery B charges approximately \(0.67\) (or \(66.67\) cents) per doughnut.
- True.
So, the true statements are:
- A
- B
- D
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