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=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+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: C=500s+75; Greenhill Country Club: C=1,000s+65
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=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
b plus c equals 2,000 ; 10 b plus 5 c equals 12,500
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+c=2,000; 10b+5c=12,500
Solve for the unknowns in the following problem: Jamal sells cookies and lemonade for his baseball team’s fundraising event. A cookie is priced at $1.25 each, and lemonade is priced at $1.00 each. Last week, Jamal sold a combined total of 45 cookies and lemonades and collected $51.75. How many of each item did Jamal sell last week?(1 point)
Responses
18 cookies and 27 lemonades
18 cookies and 27 lemonades
27 cookies and 18 lemonades
27 cookies and 18 lemonades
15 cookies and 33 lemonades
15 cookies and 33 lemonades
22 cookies and 23 lemonades
18 cookies and 27 lemonades
Let's set up a system of equations to represent the given information:
Let x be the number of cookies sold and y be the number of lemonades sold.
1.25x + 1.00y = 51.75 (total amount collected)
x + y = 45 (total number of items sold)
Now, we can solve this system of equations.
Using the elimination method,
1.25x + 1.00y = 51.75
x + y = 45 (multiply by -1.25 to eliminate x)
-1.25x - 1.25y = -56.25
0.25y = -4.50
y = 18
Substitute y back into x + y = 45
x + 18 = 45
x = 27
Therefore, Jamal sold 18 cookies and 27 lemonades last week.
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 Mania; $25
Balloon Mania; $25
Balloon Express; $25
Balloon Express; $25
Balloon Mania; $5
Let x be the number of balloons they order from Balloon Express and y be the number of balloons they order from Balloon Mania. The total cost for Balloon Express will be 2x + 10 and for Balloon Mania will be 1.50y + 20.
Given that they plan to order 30 balloons, so x + y = 30.
Let's substitute x = 30 - y and solve the equation:
2(30-y) + 10 = 1.50y + 20
60 - 2y + 10 = 1.50y + 20
-2y + 70 = 1.50y + 20
-70 - 20 = 1.50y + 2y
-90 = 3.5y
y ≈ 25.71
Since we can't order a fraction of a balloon, we will round down to 25 balloons for Balloon Mania and 5 balloons for Balloon Express.
Now, to find the total cost:
For Balloon Express: 2(5) + 10 = $20
For Balloon Mania: 1.50(25) + 20 = $57.50
Balloon Express is the cheaper option by $37.50.
Therefore, the correct response is:
Balloon Express; $37.50
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
100 hot dogs and 200 pretzels
100 hot dogs and 200 pretzels
200 hot dogs and 100 pretzels
200 hot dogs and 100 pretzels
50 hot dogs and 250 pretzels
Let x be the number of hot dogs sold and y be the number of pretzels sold.
Given:
x + y = 300 (total number of items in stock)
4x + 2y = 800 (income goal)
We can solve this system of equations:
1. x + y = 300
2. 4x + 2y = 800
From equation 1, we can solve for x:
x = 300 - y
Substitute x into equation 2:
4(300 - y) + 2y = 800
1200 - 4y + 2y = 800
-2y = -400
y = 200
Substitute y back into x + y = 300:
x + 200 = 300
x = 100
The boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.
Therefore, the correct response is:
100 hot dogs and 200 pretzels.