Answer :
### Solution:
#### Part 1: Equation for the Total Cost of Pizzas
To determine the total cost \( T \) of \( c \) large cheese pizzas and \( d \) large one-topping pizzas, we can use the following information:
- Each large cheese pizza costs \$5.
- Each large one-topping pizza costs \$6.
The equation representing the total cost \( T \) is:
[tex]\[ T = 5c + 6d \][/tex]
#### Part 2: Representing Quantities and Constraints
For the book club meeting, we need to consider the quantities and constraints given:
- Jada is preparing for 15 people.
- Each person needs 12 ounces of milk.
- Each person gets 4 cookies.
- A package of cookies contains 24 cookies.
- A 1-gallon jug of milk contains 128 ounces and costs \$3.
We will create equations that link these quantities and constraints.
Equation A: Total Ounces of Milk Needed
[tex]\[ m = 12 \times 15 \][/tex]
Each of the 15 people needs 12 ounces of milk, so:
[tex]\[ m = 180 \][/tex]
Equation B: Budget Equation Combining Milk and Cookies
[tex]\[ 3m + 4.5c = b \][/tex]
The cost of milk is \[tex]$3 per gallon, and the cost of cookies is \$[/tex]4.50 per package.
Equation C: Total Cookies Needed
[tex]\[ 4n = c \][/tex]
Since each of the 15 people (including Jada) gets 4 cookies:
[tex]\[ c = 4 \times 15 \][/tex]
[tex]\[ c = 60 \][/tex]
Equation D: Number of Cookies in Terms of Packages
[tex]\[ c = 4 \text{ packages} \][/tex]
Although this is written differently, it signifies the total number of cookies equivalent to 4 packages, with each package containing 24 cookies:
[tex]\[ c = 4 \times 24 = 96 \][/tex]
Equation E: Calculation of Budget for Specific Values \( n = 2 \) and \( m = 3 \)
[tex]\[ b = 2 \times 3 + 3 \times 4.5 \][/tex]
[tex]\[ b = 6 + 13.5 \][/tex]
[tex]\[ b = 19.5 \][/tex]
Here are the corresponding equations:
1. Total Cost of Pizzas:
[tex]\[ T = 5c + 6d \][/tex]
2. Equations from Book Club Scenario:
- Total ounces of milk needed:
[tex]\[ m = 12 \times 15 \][/tex]
- Budget equation:
[tex]\[ 3m + 4.5c = b \][/tex]
- Total cookies needed:
[tex]\[ 4n = c \][/tex]
- Number of cookies as packages:
[tex]\[ c = 4 \text{ packages} \][/tex]
- Budget calculation for specific values:
[tex]\[ b = 2 \times 3 + 3 \times 4.5 \][/tex]
Thus, the selected equations representing the quantities and constraints in this situation are:
- A. \( m = 12 \times 15 \)
- B. \( 3m + 4.5c = b \)
- C. \( 4n = c \)
- E. \( b = 2 \times 3 + 3 \times 4.5 \)
These equations cover the total amount of milk, budget considerations, total cookies needed, and a budget calculation verifying specific values.
#### Part 1: Equation for the Total Cost of Pizzas
To determine the total cost \( T \) of \( c \) large cheese pizzas and \( d \) large one-topping pizzas, we can use the following information:
- Each large cheese pizza costs \$5.
- Each large one-topping pizza costs \$6.
The equation representing the total cost \( T \) is:
[tex]\[ T = 5c + 6d \][/tex]
#### Part 2: Representing Quantities and Constraints
For the book club meeting, we need to consider the quantities and constraints given:
- Jada is preparing for 15 people.
- Each person needs 12 ounces of milk.
- Each person gets 4 cookies.
- A package of cookies contains 24 cookies.
- A 1-gallon jug of milk contains 128 ounces and costs \$3.
We will create equations that link these quantities and constraints.
Equation A: Total Ounces of Milk Needed
[tex]\[ m = 12 \times 15 \][/tex]
Each of the 15 people needs 12 ounces of milk, so:
[tex]\[ m = 180 \][/tex]
Equation B: Budget Equation Combining Milk and Cookies
[tex]\[ 3m + 4.5c = b \][/tex]
The cost of milk is \[tex]$3 per gallon, and the cost of cookies is \$[/tex]4.50 per package.
Equation C: Total Cookies Needed
[tex]\[ 4n = c \][/tex]
Since each of the 15 people (including Jada) gets 4 cookies:
[tex]\[ c = 4 \times 15 \][/tex]
[tex]\[ c = 60 \][/tex]
Equation D: Number of Cookies in Terms of Packages
[tex]\[ c = 4 \text{ packages} \][/tex]
Although this is written differently, it signifies the total number of cookies equivalent to 4 packages, with each package containing 24 cookies:
[tex]\[ c = 4 \times 24 = 96 \][/tex]
Equation E: Calculation of Budget for Specific Values \( n = 2 \) and \( m = 3 \)
[tex]\[ b = 2 \times 3 + 3 \times 4.5 \][/tex]
[tex]\[ b = 6 + 13.5 \][/tex]
[tex]\[ b = 19.5 \][/tex]
Here are the corresponding equations:
1. Total Cost of Pizzas:
[tex]\[ T = 5c + 6d \][/tex]
2. Equations from Book Club Scenario:
- Total ounces of milk needed:
[tex]\[ m = 12 \times 15 \][/tex]
- Budget equation:
[tex]\[ 3m + 4.5c = b \][/tex]
- Total cookies needed:
[tex]\[ 4n = c \][/tex]
- Number of cookies as packages:
[tex]\[ c = 4 \text{ packages} \][/tex]
- Budget calculation for specific values:
[tex]\[ b = 2 \times 3 + 3 \times 4.5 \][/tex]
Thus, the selected equations representing the quantities and constraints in this situation are:
- A. \( m = 12 \times 15 \)
- B. \( 3m + 4.5c = b \)
- C. \( 4n = c \)
- E. \( b = 2 \times 3 + 3 \times 4.5 \)
These equations cover the total amount of milk, budget considerations, total cookies needed, and a budget calculation verifying specific values.
