Question

Scenario:

Athena has $44.95 to spend at a bakery for her holiday party. The bakery charges $2.75 per slice of chocolate mousse cake. They also charge a fee of $3.15 to wrap your cake as a gift.

a) Write a let statement that can be used to solve the problem.
Please write a "let" statement that can be used to solve this problem.

b) Set up an equation that can be used to determine how many slices of cake Athena can buy.
Set up an equation that can be used to determine the number of slices of chocolate mousse cake Athena can buy with her budget.

c) Solve your equation. Just type the number in your solution. For example, if x=5, just type "5".
Solve the equation you set up in 7b and provide the numerical solution.

d) Analyze your solution in the context of the problem. How many slices of cake can Athena afford to buy?
Analyze your solution in the context of the problem and state how many slices of chocolate mousse cake Athena can afford to buy with her budget. Additionally, include a check to ensure your work is accurate.




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Answer 1

Athena can afford to buy 15 slices of chocolate mousse cake with her budget of $44.95 after accounting for the gift wrapping fee. The equation to find the number of slices is 2.75x + 3.15 = 44.95, and after solving, x = 15.2, which must be rounded down to a whole number of slices.

Step-by-step explanation:

Let Statement and Equation Setup:

Let x be the number of slices of chocolate mousse cake Athena can buy.

The equation to determine the number of slices Athena can buy is:

2.75x + 3.15 = 44.95

Solving the Equation:

x = (44.95 - 3.15) / 2.75

x = 41.80 / 2.75

x = 15.2

Analyzing the Solution:

Since Athena cannot buy a fraction of a slice, she can afford to buy 15 slices of chocolate mousse cake, with some money left over that is not enough to buy an additional slice. To check the accuracy, multiply the number of slices (15) by the price per slice (2.75) and add the wrapping fee (3.15):

(15 * 2.75) + 3.15 = 41.25 + 3.15 = 44.40

Therefore, Athena has spent $44.40, which is within her budget of $44.95.