Sue is planning a shopping trip to get holiday gifts for her friends and family. She decides to get each person of $20 Reese restaurant gift card. She also wants to pick up some more toys for her dog which will cost $17 off which function model the situation.

Question

f(x) = 17 + 20^x
f(x) = 17x + 20
f(x) - 20x + 17
f(x) - 17(20)^x
How much money can sue expect to spend if she shops for six people and her dog?

Answer 1

To determine how much money Sue can expect to spend, we need to calculate the total costs based on her plans:

1. Cost of the gift cards for six people: Each gift card costs $20, and she is buying one for each of the six people. \[ \text{Total for gift cards} = 6 \times 20 = 120 \text{ dollars} \]

2. Cost of toys for her dog: The toys for her dog will cost $17. \[ \text{Total for dog toys} = 17 \text{ dollars} \]

3. Total cost: Add the total cost of the gift cards and the cost of the toys for her dog. \[ \text{Total Cost} = \text{Total for gift cards} + \text{Total for dog toys} = 120 + 17 = 137 \text{ dollars} \]

Therefore, Sue can expect to spend $137.

Function Model Analysis

To express this scenario mathematically, let's evaluate the function models provided, focusing on how her spending can be modeled.

• If x represents the number of people she buys gift cards for, then her total spending can be represented by:
  • \( f(x) = 20x + 17 \)
  • This function reflects the total spending based on the number of gift cards (20 per person) plus the cost of the dog toys (17).

Thus, the correct function model for the situation is: \[ f(x) = 20x + 17 \]

When \( x = 6 \) (the number of people): \[ f(6) = 20(6) + 17 = 120 + 17 = 137 \] This confirms her total expense of $137 when shopping for six people and her dog.