Activity

Question

Rylee shopped at a clothing store, where she spent $36.50 plus 8% tax. Then, she spent $25 to refuel her car at the gas station. Finally, she bought groceries worth $23.50. At the grocery checkout, she handed over a coupon for a 20% discount on her purchase.

Complete the following steps to help Rylee find the net change to her banking account balance.

Part A
Use decimal numbers to write an expression that represents the net change in Rylee’s bank account balance after paying for her purchase at the clothing store.

Space used (includes formatting): 0 / 30000
Part B
Write an expression that represents the net change in Rylee’s bank account balance after paying for fuel at the gas station.

Space used (includes formatting): 0 / 30000
Part C
Use decimal numbers to write an expression that represents the net change in Rylee’s bank account balance after paying for groceries.

Space used (includes formatting): 0 / 30000
Part D
Finally, use decimal numbers to write an expression that represents the net change in Rylee’s bank account balance for her entire shopping trip. Use your answers from parts A through C to guide you.

Space used (includes formatting): 0 / 30000
Part E
Simplify the expression in part D to find the net change in Rylee’s bank account balance. Express your answer as a decimal number.

Space used (includes formatting): 0 / 30000
Self-Evaluation
How did you do? Rate your work on a scale of 1 to 5, with 5 as the highest score. Then write a brief evaluation of your work below. Note what you learned and what challenged you.

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Answer 1

To help Rylee find the net change to her banking account balance after her purchases, let's break down each part step by step.

Part A: Clothing Store

1. Rylee spent $36.50 on clothes.
2. The tax on her purchase is 8% of $36.50, which is calculated as follows: \[ \text{Tax} = 0.08 \times 36.50 = 2.92 \]
3. The total spending at the clothing store is: \[ 36.50 + 2.92 = 39.42 \]

Expression for Part A: \[

• (36.50 + 0.08 \times 36.50) \] or \[
• 39.42 \]

Part B: Gas Station

1. Rylee spent $25 to refuel her car.

Expression for Part B: \[

• 25 \]

Part C: Groceries

1. Rylee bought groceries worth $23.50.
2. She used a coupon for a 20% discount. First, we calculate the discount: \[ \text{Discount} = 0.20 \times 23.50 = 4.70 \]
3. The total spending after the discount is: \[ 23.50 - 4.70 = 18.80 \]

Expression for Part C: \[

• (23.50 - 0.20 \times 23.50) \] or \[
• 18.80 \]

Part D: Total Net Change

Now, we combine the expressions from Parts A, B, and C for the total net change:

\[ \text{Total Net Change} = -(36.50 + 0.08 \times 36.50) - 25 - (23.50 - 0.20 \times 23.50) \]

Substituting in the total amounts: \[ = -39.42 - 25 - 18.80 \]

Part E: Simplification

Now we simplify the expression:

1. Combine the values: \[ -39.42 - 25 - 18.80 = -83.22 \]

Final Answer for Part E: \[ -83.22 \]

Self-Evaluation

On a scale of 1 to 5, I would rate my work a 5. I clearly broke down the calculations for each of Rylee's purchases, ensured I included tax and discounts properly, and correctly simplified the total expenditure to find the net change in her account balance. I learned to carefully manage multiple transactions and perform the necessary calculations step by step, which is crucial in real-life budgeting and finance. The challenge was ensuring I accounted for the tax and discount correctly.