QuestionHS Algebra 2 UO Quick Quiz \#1 - 24-25 / 6 OF 8 on 6 - Notes Line Guide Reset Answer
This question has many parts. Be sure to answer all the parts of the question.
A sandwich shop charges one price for any foot-long sub, with the option of adding premium toppings for $\$ 1.30$ each. A foot-long sub with 2 premium toppings costs \ $9.09. Adrienne and Riley are asked to write an explicit rule for the cost of a footlong sandwich with$ n $premium toppings. Their answers are shown below. Adrienne:$ f(n)=9.09+1.30(n-2) $Riley:$ f(n)=6.49+1.30 n$ Review/ End Test Flag I Options Back Naxt

Studdy Solution

STEP 1

1. The base price of a foot-long sub without premium toppings needs to be determined.
2. Each premium topping costs an additional \$1.30.
3. A foot-long sub with 2 premium toppings costs \$9.09.

STEP 2

1. Determine the base price of the sandwich without any premium toppings.
2. Verify Adrienne's rule for correctness.
3. Verify Riley's rule for correctness.
4. Compare both rules and conclude which one is correct.

STEP 3

To find the base price of the sandwich without premium toppings, we start with the given information: a sandwich with 2 premium toppings costs \$9.09.
Calculate the cost of the 2 premium toppings: $\text{Cost of 2 toppings} = 2 \times 1.30 = 2.60$
Subtract the cost of the 2 premium toppings from the total cost to find the base price: $\text{Base price} = 9.09 - 2.60 = 6.49$

STEP 4

Verify Adrienne's rule: $f(n) = 9.09 + 1.30(n - 2)$
Substitute $n = 2$ to check if it matches the given cost: $f(2) = 9.09 + 1.30(2 - 2) = 9.09 + 0 = 9.09$
Adrienne's rule correctly calculates the cost for 2 toppings.

STEP 5

Verify Riley's rule: $f(n) = 6.49 + 1.30n$
Substitute $n = 2$ to check if it matches the given cost: $f(2) = 6.49 + 1.30 \times 2 = 6.49 + 2.60 = 9.09$
Riley's rule also correctly calculates the cost for 2 toppings.

STEP 6

Both Adrienne's and Riley's rules correctly calculate the cost of a sandwich with 2 premium toppings. However, Riley's rule directly uses the base price and adds the cost of $n$ toppings, which is simpler and more intuitive.
Therefore, Riley's rule is the explicit rule for the cost of a footlong sandwich with $n$ premium toppings: $f(n) = 6.49 + 1.30n$
The correct explicit rule is:
$\boxed{f(n) = 6.49 + 1.30n}$

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