Answered

At the fast food restaurant, an order of fries costs $1.14 and a drink costs $1.22.


  1. How much would it cost to get 4 orders of fries and 3 drinks?
  2. How much would it cost to get f orders of fries and d drinks?

Verified Answer :

  • The cost of one order of fries is \(\$1.14\), and the cost of one drink is \(\$1.22\).
  • The total cost for 4 orders of fries and 3 drinks is calculated as \(4 \times 1.14 + 3 \times 1.22 = \boxed{\$8.22}\).
  • The general formula for the cost of \(f\) orders of fries and \(d\) drinks is \(\boxed{T = 1.14f + 1.22d}\).

Explanation

  1. Data Analysis

We have the unit costs for two items at a fast food restaurant:

  • One order of fries costs \(C_f = \$1.14\).
  • One drink costs \(C_d = \$1.22\).

Our goal is to calculate the total cost for a specific order (4 fries and 3 drinks) and to generalize this into a formula for any number of orders \(f\) and drinks \(d\).

  1. Calculating the Specific Order Cost

To find the total cost of 4 orders of fries and 3 drinks, we multiply the quantity of each item by its unit cost and sum them:

  • Cost of 4 fries: \(4 \times \$1.14 = \$4.56\).
  • Cost of 3 drinks: \(3 \times \$1.22 = \$3.66\).

Adding these together, the total cost is \(\$4.56 + \$3.66 = \$8.22\).

  1. Generalizing the Cost Formula

To generalize the cost calculation for any quantity of fries \(f\) and any number of drinks \(d\), we represent the total cost \(T\) as a linear combination of the unit costs:
\[T = f \times C_f + d \times C_d\]
Substituting the known values for \(C_f\) and \(C_d\):
\[T = 1.14f + 1.22d\]
This formula allows for calculating the cost for any combination of items at the restaurant.

Examples

This type of cost calculation is used every day when shopping or dining. By assigning unit costs to items (like items on a menu or groceries), you can quickly estimate total expenses or set a budget for your purchases. For example, if you know the price of a burger is \(\$5.00\) and a soda is \(\$2.00\), you can use the formula \(T = 5.00b + 2.00s\) to determine the total price for any number of burgers \(b\) and sodas \(s\), helping you manage your spending effectively.

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