Regal Hotel: C = 500s + 75
Greenhill Country Club: C = 1,000s + 65
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 , $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=1,000s+75; Greenhill Country Club: C=500s+65 Regal Hotel: upper C equals 1,000 s plus 75 ; Greenhill Country Club: upper C equals 500 s plus 65 Regal Hotel: C=75s+1,000; Greenhill Country Club: C=65s+500
9 answers
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; 10b+5c=12,500 b plus c equals 2,000 ; 10 b plus 5 c equals 12,500 b+c=2,000; 5b+10c=12,500
b + c = 2,000
10b + 5c = 12,500
10b + 5c = 12,500
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; $25 Balloon Express; $25 Balloon Mania; $25 Balloon Mania; $25 Balloon Express; $5 Balloon Express; $5 Balloon Mania; $5
Let's set up a system of equations:
Let x be the number of balloons and y be the total cost.
For Balloon Express: y = 2x + 10
For Balloon Mania: y = 1.50x + 20
Since the O'Donnells plan to order 30 balloons, we can substitute x = 30 into the equations:
For Balloon Express: y = 2(30) + 10 = 60 + 10 = 70
For Balloon Mania: y = 1.50(30) + 20 = 45 + 20 = 65
Therefore, the O'Donnells should choose Balloon Mania, and they will save $5.
Let x be the number of balloons and y be the total cost.
For Balloon Express: y = 2x + 10
For Balloon Mania: y = 1.50x + 20
Since the O'Donnells plan to order 30 balloons, we can substitute x = 30 into the equations:
For Balloon Express: y = 2(30) + 10 = 60 + 10 = 70
For Balloon Mania: y = 1.50(30) + 20 = 45 + 20 = 65
Therefore, the O'Donnells should choose Balloon Mania, and they will save $5.
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 20 quiches 20 quiches 12 quiches 12 quiches 45 quiches 45 quiches 75 quiches 75 quiches
Let x be the number of quiches they need to sell to break even.
The cost to make x quiches is 30 + 0.50x and the revenue from selling x quiches is 2x.
To break even, the cost equals the revenue:
30 + 0.50x = 2x
Solve for x:
30 = 2x - 0.50x
30 = 1.50x
x = 30 / 1.50
x = 20
Therefore, the Spanish Club at Santa Fe Middle School will need to sell 20 quiches in order to break even.
The cost to make x quiches is 30 + 0.50x and the revenue from selling x quiches is 2x.
To break even, the cost equals the revenue:
30 + 0.50x = 2x
Solve for x:
30 = 2x - 0.50x
30 = 1.50x
x = 30 / 1.50
x = 20
Therefore, the Spanish Club at Santa Fe Middle School will need to sell 20 quiches in order to break even.
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 50 hot dogs and 250 pretzels 50 hot dogs and 250 pretzels 100 hot dogs and 200 pretzels 100 hot dogs and 200 pretzels 250 hot dogs and 50 pretzels 250 hot dogs and 50 pretzels 200 hot dogs and 100 pretzels
Let's use a system of equations to solve this problem:
Let h be the number of hot dogs and p be the number of pretzels.
We can set up the following equations based on the given information:
h + p = 300 (Equation 1)
4h + 2p = 800 (Equation 2)
Now, we can solve the system of equations:
From Equation 1, we can rewrite it as h = 300 - p and substitute it into Equation 2:
4(300 - p) + 2p = 800
1200 - 4p + 2p = 800
-2p = -400
p = 200
Now, we can substitute p = 200 back into h = 300 - p:
h = 300 - 200
h = 100
Therefore, the Baynard High School Boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.
Let h be the number of hot dogs and p be the number of pretzels.
We can set up the following equations based on the given information:
h + p = 300 (Equation 1)
4h + 2p = 800 (Equation 2)
Now, we can solve the system of equations:
From Equation 1, we can rewrite it as h = 300 - p and substitute it into Equation 2:
4(300 - p) + 2p = 800
1200 - 4p + 2p = 800
-2p = -400
p = 200
Now, we can substitute p = 200 back into h = 300 - p:
h = 300 - 200
h = 100
Therefore, the Baynard High School Boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.
9 answers