The senior class at Hartford High School is planning their prom. They’ve narrowed the location down to two choices. The Regal Hotel charges, C

Question

, $500 for the ballroom rental fee and $75 per student, s
, for the meal. The Greenhill Country Club charges, C
, $1,000 for the ballroom rental fee and $65 per student, s
, for the meal. Create a pair of linear equations that represent this real-world problem.(1 point)
Responses

Regal Hotel: C=500s+75
; Greenhill Country Club: C=1,000s+65
Regal Hotel: upper C equals 500 s plus 75 ; Greenhill Country Club: upper C equals 1,000 s plus 65

Regal Hotel: C=75s+500
; Greenhill Country Club: C=65s+1,000
Regal Hotel: upper C equals 75 s plus 500 ; Greenhill Country Club: upper C equals 65 s plus 1,000

Regal Hotel: C=75s+1,000
; Greenhill Country Club: C=65s+500
Regal Hotel: upper C equals 75 s plus 1,000 ; Greenhill Country Club: upper C equals 65 s plus 500

Regal Hotel: C=1,000s+75
; Greenhill Country Club: C=500s+65

Answer 1

To create the linear equations that represent the costs for the two locations, let's denote the total cost as \( C \) and the number of students as \( s \).

1. Regal Hotel:

   • The total cost includes a fixed ballroom rental fee of $500 and a cost of $75 per student.
   • The equation is: \[ C = 75s + 500 \]

2. Greenhill Country Club:

   • The total cost includes a fixed ballroom rental fee of $1,000 and a cost of $65 per student.
   • The equation is: \[ C = 65s + 1000 \]

Thus, the correct pair of linear equations is:

• Regal Hotel: \( C = 75s + 500 \)
• Greenhill Country Club: \( C = 65s + 1000 \)

So the second pair of equations matches this and is the correct answer:

• Regal Hotel: \( C = 75s + 500 \); Greenhill Country Club: \( C = 65s + 1000 \).

Answer 2

The Jackson Jammers are giving away bags and caps at their next game. The bags, b, cost them $10 each, and the caps, c, cost them $5 each. They plan to give away 2,000 total items and have a budget of $12,500. Write the pair of linear equations that model this situation.(1 point)
Responses

b+c=12,500; 10b+5c=2,000
b plus c equals 12,500 ; 10 b plus 5 c equals 2,000

b+c=12,500; 5b+10c=2,000
b plus c equals 12,500 ; 5 b plus 10 c equals 2,000

b+c=2,000; 5b+10c=12,500
b plus c equals 2,000 ; 10 b plus 10 c equals 12,500

b+c=2,000; 10b+5c=12,500

Answer 3

To model the situation of the Jackson Jammers giving away bags and caps, we need to set up the equations based on the given information regarding the total number of items and the budget.

Let:

• \( b \) = number of bags
• \( c \) = number of caps

From the problem, we know:

1. The total number of items (bags and caps) they plan to give away is 2,000: \[ b + c = 2000 \]

2. The total cost must not exceed the budget of $12,500. The cost for the bags is $10 each, and the cost for the caps is $5 each: \[ 10b + 5c = 12500 \]

So, the correct pair of linear equations that model this situation is:

• \( b + c = 2000 \)
• \( 10b + 5c = 12500 \)

Thus, the correct response is:

• b + c = 2000; 10b + 5c = 12,500.

Answer 4

Solve this real-world problem using a system of equations. The O’Donnells are having a birthday party for their son, and they plan to have a clown bring balloons to the party. Balloon Express charges $2 per balloon and $10 for delivery. Balloon Mania charges $1.50 per balloon and $20 for delivery. If the O’Donnells plan to order 30 balloons, which company should they choose, and how much will they save?(1 point)
Responses

Balloon Express; $5
Balloon Express; $5

Balloon Express; $25
Balloon Express; $25

Balloon Mania; $5
Balloon Mania; $5

Balloon Mania; $25 

Answer 5

To determine which balloon company the O’Donnells should choose, we need to set up the total cost equations for each company based on the price per balloon and the delivery fee.

Let’s calculate the total cost for each company using the following formulas:

1. Balloon Express:

   • Cost per balloon: $2
   • Delivery fee: $10
   • Total cost, \( C_E \), for 30 balloons: \[ C_E = (2 \times 30) + 10 = 60 + 10 = 70 \]

2. Balloon Mania:

   • Cost per balloon: $1.50
   • Delivery fee: $20
   • Total cost, \( C_M \), for 30 balloons: \[ C_M = (1.50 \times 30) + 20 = 45 + 20 = 65 \]

Now we have:

• Total cost for Balloon Express: $70
• Total cost for Balloon Mania: $65

Next, we need to determine which company is cheaper and how much the O'Donnells will save:

• Savings: \[ \text{Savings} = C_E - C_M = 70 - 65 = 5 \]

Thus, the O’Donnells should choose Balloon Mania, and they will save $5.

The correct response is:

• Balloon Mania; $5.

Answer 6

The Spanish Club at Santa Fe Middle School wants to sell mini quiches to raise money for a field trip. The culinary department at their school will make the quiches for $30 plus $0.50 per quiche for the ingredients. The Spanish Club wants to sell each quiche for $2. How many quiches will they need to sell in order to break even?(1 point)
Responses

75 quiches
75 quiches

45 quiches
45 quiches

12 quiches
12 quiches

20 quiches

Answer 7

To find out how many quiches the Spanish Club needs to sell in order to break even, we need to set up equations representing their costs and revenues.

1. Cost of making the quiches:

   • Fixed cost: $30
   • Variable cost per quiche: $0.50
   • If \( q \) is the number of quiches made, then the total cost \( C \) can be represented as: \[ C = 30 + 0.50q \]

2. Revenue from selling the quiches:

   • Selling price per quiche: $2
   • The total revenue \( R \) can be represented as: \[ R = 2q \]

3. Break-even point: To break even, the total cost should equal the total revenue: \[ 30 + 0.50q = 2q \]

Now, we can solve for \( q \): \[ 30 = 2q - 0.50q \] \[ 30 = 1.5q \] \[ q = \frac{30}{1.5} = 20 \]

Thus, the Spanish Club needs to sell 20 quiches in order to break even.

The correct response is:

• 20 quiches.

Answer 8

The Baynard High School Boosters are selling hot dogs and pretzels at the concession stand. They have 300 hot dogs and pretzels in stock and want to earn an income of $800. They plan to sell the hot dogs for $4 each and the pretzels for $2 each. How many hot dogs and how many pretzels do the boosters need to sell to reach their goal of $800?(1 point)
Responses

250 hot dogs and 50 pretzels
250 hot dogs and 50 pretzels

200 hot dogs and 100 pretzels
200 hot dogs and 100 pretzels

50 hot dogs and 250 pretzels
50 hot dogs and 250 pretzels

100 hot dogs and 200 pretzels

Answer 9

To determine how many hot dogs and pretzels the Baynard High School Boosters must sell to reach their income goal of $800, let's define the number of hot dogs sold as \( h \) and the number of pretzels sold as \( p \).

We have the following two equations based on the problem:

1. Total number of hot dogs and pretzels: \[ h + p = 300 \]

2. Total income from selling hot dogs and pretzels: \[ 4h + 2p = 800 \]

Now we can solve this system of equations.

First, we can solve the first equation for \( p \): \[ p = 300 - h \]

Now, substitute \( p \) into the second equation: \[ 4h + 2(300 - h) = 800 \] \[ 4h + 600 - 2h = 800 \] \[ 2h + 600 = 800 \] \[ 2h = 800 - 600 \] \[ 2h = 200 \] \[ h = 100 \]

Now substitute \( h = 100 \) back into the equation for \( p \): \[ p = 300 - 100 = 200 \]

So, the boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.

The correct response is:

• 100 hot dogs and 200 pretzels.