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, C, $1,000 for the ballroom rental fee and $65 per student, s, for the meal. Create a pair of linear equations that represents this real-world problem.
A. Regal Hotel: C = 75s + 1,000; Greenhill Country Club: C = 65s + 500
B. Regal Hotel: C = 500s + 75; Greenhill Country Club: C = 1,000s + 65
C. Regal Hotel: C = 75s + 500; Greenhill Country Club: C = 65s + 1,000
D. Regal Hotel: C = 1,000s + 75; Greenhill Country Club: C = 500s + 65
C. Regal Hotel: C = 75s + 500; Greenhill Country Club: C = 65s + 1,000
The jackson jammmers 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.
A. b + c =2,000; 5b + 10c =12,500
B. b + c =12,500; 10b + 5c = 2,000
C. b + c =2,000; 10b + 5c = 12,500
D. b + c = 12,500; 5b + 10c = 2,000
A. b + c =2,000; 5b + 10c =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 mania charges 1.50 per balloon and $20 for delivery. if the o'donnells plan to order 3 balloons, whoch company should they choose, and how much will they save?
A. Balloon Express; $25
B. Balloon Express; $5
C. Balloon Mania; $5
D.Balloon Mania; $25
Let's set up a system of equations to solve this problem.
Let's use B to represent the number of balloons and C to represent the cost.
For Balloon Express: C = 1.50B + 20
For Balloon Mania: C = 3B
Since the O'Donnells plan to order 3 balloons, we can substitute B = 3 into the equations.
For Balloon Express: C = 1.50(3) + 20 = 4.50 + 20 = 24.50
For Balloon Mania: C = 3(3) = 9
Therefore, the O'Donnells should choose Balloon Mania, as it will cost them $9. By choosing Balloon Mania, they will save $15.50 compared to Balloon Express.
Answer: D. Balloon Mania; $25
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?
A. 75 quiches
B. 45quiches
C. 20quiches
D. 12 quiches
Let's set up the equation to find the break-even point.
Let's represent the number of quiches as Q and the cost as C.
The cost equation would be: C = 30 + 0.50Q
The revenue equation would be: R = 2Q
To break even, the cost must equal the revenue. So we have:
30 + 0.50Q = 2Q
Let's solve for Q:
30 = 2Q - 0.50Q
30 = 1.50Q
Q = 30 / 1.50
Q = 20
Therefore, they will need to sell 20 quiches in order to break even.
Answer: C. 20 quiches
You are trying to guess the code to a puzzle while participating in an escape room. There are two buttons, blue and red, and you have put the correct number in each one to unlock the door to the next room. There are only two clues to help you:
Clue 1: If you double the blue number and add it to the red number, you get 6.
Clue 2: If you quadruple the blue number and add it to double to the red number, you get 12
You only get two attempts at the puzzle, and if you getvit wrong, the game will be over. Use the system of equations shown to determine how many solutions there are to this puzzle.
{ 2b + r = 6
{ 4b + 2r = 12
A. There are infinitely many solutions.
B. there is only one solution.
C. There are only two solutions.
D. There is no solution.
Let's solve the system of equations to determine the number of solutions.
{ 2b + r = 6
{ 4b + 2r = 12
We can use the method of elimination to solve for the variables. Let's multiply the first equation by 2 to make the coefficients of 'r' the same:
{ 4b + 2r = 12
{ 4b + 2r = 12
By subtracting the first equation from the second equation, we can eliminate 'b':
4b + 2r - (2b + r) = 12 - 6
2b + r = 6
The resulting equation 2b + r = 6 is the same as the first equation, which means the two equations are actually the same equation. This implies that there are infinitely many solutions to this puzzle.
Answer: A. There are infinitely many solutions.
The correct pair of linear equations that represents this real-world problem is:
C. Regal Hotel: C = 75s + 500; Greenhill Country Club: C = 65s + 1,000
To find the correct pair of linear equations, we need to examine the information given.
For the Regal Hotel, we are given that the ballroom rental fee is $500, represented by C, and the meal cost per student is $75, represented by s. The total cost, C, can be calculated by adding the rental fee and the product of the meal cost and the number of students: C = 75s + 500.
For the Greenhill Country Club, we are given that the ballroom rental fee is $1,000, represented by C, and the meal cost per student is $65, represented by s. The total cost, C, can be calculated by adding the rental fee and the product of the meal cost and the number of students: C = 65s + 1,000.
Therefore, the correct pair of linear equations that represents this real-world problem is C = 75s + 500 for the Regal Hotel, and C = 65s + 1,000 for the Greenhill Country Club, which matches option C.