Question

lesson practice problems

1. large cheese pizzas cost $5 each and large one - topping pizzas cost $6 each. write an equation that represents the total cost, t, of c large cheese pizzas and d large one - topping pizzas.
2. jada plans to serve milk and healthy cookies for a book club meeting. she is preparing 12 ounces of milk and 4 cookies per person. including herself, there are 15 people in the club. a package of cookies contains 24 cookies and costs $4.50. a 1 - gallon jug of milk contains 128 ounces and costs $3. let n represent the number of people in the club, m represent the ounces of milk, c represent the number of cookies, and b represent jadas budget in dollars. circle all of the equations that could represent the quantities and constraints in this situation.

a m = 12(15)
b 3m + 4.5c = b
c 4n = c
d 4(4.50)=c
e b = 2(3)+3(4.50)

Explanation:

Step1: Analyze pizza - cost problem

The cost of $c$ large cheese pizzas at $5$ dollars each is $5c$, and the cost of $d$ large one - topping pizzas at $6$ dollars each is $6d$. The total cost $T$ is the sum of these two costs.
$T = 5c+6d$

Step2: Analyze milk - cookie problem

1. For the milk quantity:

• Since she is preparing 12 ounces of milk per person and there are 15 people, the total ounces of milk $m$ is given by $m = 12\times15$. So option A is correct.

1. For the cookie - person relationship:

• She is preparing 4 cookies per person. If $n$ is the number of people and $c$ is the number of cookies, then $c = 4n$. So option C is correct.

1. For the budget:

• A 1 - gallon jug of milk contains 128 ounces and costs $3$, and a package of cookies contains 24 cookies and costs $4.50$.
• There are 15 people, so she needs $\frac{12\times15}{128}\approx1.41$ jugs of milk (we'll consider whole jugs for simplicity), and $\frac{4\times15}{24}=2.5$ packages of cookies.
• The budget $b$ is the cost of milk and cookies. The cost of 2 jugs of milk is $2\times3$ and the cost of 3 packages of cookies is $3\times4.50$. So $b = 2\times3+3\times4.50$. Option E is correct.
• Option B is incorrect because there is no such linear relationship between $m$, $c$, and $b$ based on the given costs and quantities. Option D is incorrect as $4\times4.50$ does not represent the number of cookies.

Answer:

1. $T = 5c + 6d$
2. A. $m = 12(15)$

C. $4n = c$
E. $b = 2(3)+3(4.50)$