Equation for Bowl-O-Rama: C = 5g + 4
Equation for Bowling Pinz: C = 4g + 8
The cost, C, to bowl at Bowl-O-Rama is $5 per game, g, plus $4 for shoe rental. The cost, C, to bowl at Bowling Pinz is $4 per game, g, plus $8 for shoe rental. Write the pair of linear equations that model this situation. (1 point)
Equation to represent the cost at Bowl-O-Rama: C'= ?
Equation to represent the cost at Bowling Pinz: C'= ?
11 answers
At the Henderson Middle School awards ceremony, the principal is going to honor outstanding students with gift cards. The gift cards for excellent grades, g, are worth $40, and the gift cards for perfect attendance, a, are worth $25. The principal has $4,000 allotted for this event, and he is going to recognize 100 students. Write the pair of linear equations that model this situation. (1 point)
Equation to represent the total number of students: ? = 100
Equation to represent the total cost of the gift cards: ? = 4,000
Equation to represent the total number of students: ? = 100
Equation to represent the total cost of the gift cards: ? = 4,000
Equation for the total number of students: g + a = 100
Equation for the total cost of the gift cards: 40g + 25a = 4000
Equation for the total cost of the gift cards: 40g + 25a = 4000
The Highland Booster Club sells refreshments at the concession stand for local football games. Combination 1 includes 4 hot dogs and 2 sodas for $10. Combination 2 includes 6 hot dogs and 3 sodas for $15. Let h represent the cost of a hot dog, and let s represent the cost of a soda. Write the pair of linear equations that model this situation. (1 point)
Equation for Combination 1: ? = 10
Equation for Combination 2: ? = 15
Equation for Combination 1: ? = 10
Equation for Combination 2: ? = 15
Equation for Combination 1: 4h + 2s = 10
Equation for Combination 2: 6h + 3s = 15
Equation for Combination 2: 6h + 3s = 15
Mrs. Gonzalez is going to rent a car for a business trip for one week. The total cost, C, for Top-Notch Car Rental is $150 plus $0.35 per mile, m. The total cost, C, for Fleetwood Car Rental is $200 and $0.10 per mile, m. Which company is less expensive for a 300-mile trip and by how much? Use 1 for Top-Notch Car Rental and 2 for Fleetwood Car Rental in the answer. (1 point)
The less expensive company is ? by $?
The less expensive company is ? by $?
For Top-Notch Car Rental:
C = $150 + $0.35m
Let m = 300 miles
C = $150 + $0.35(300)
C = $150 + $105
C = $255
For Fleetwood Car Rental:
C = $200 + $0.10m
Let m = 300 miles
C = $200 + $0.10(300)
C = $200 + $30
C = $230
Fleetwood Car Rental is less expensive for a 300-mile trip by $25.
So, the less expensive company is 2 (Fleetwood Car Rental) by $25.
C = $150 + $0.35m
Let m = 300 miles
C = $150 + $0.35(300)
C = $150 + $105
C = $255
For Fleetwood Car Rental:
C = $200 + $0.10m
Let m = 300 miles
C = $200 + $0.10(300)
C = $200 + $30
C = $230
Fleetwood Car Rental is less expensive for a 300-mile trip by $25.
So, the less expensive company is 2 (Fleetwood Car Rental) by $25.
Akeem wants to have a lemonade stand at the community fair. It costs him $2 to make each cup of lemonade plus a $40 renter's fee for the stand. He sells the lemonade for $6 per cup. How many cups does Akeem have to sell to break even? (1 point)
? cups
? cups
Let x be the number of cups Akeem needs to sell to break even.
The total cost for x cups is:
Total Cost = Cost to make 1 cup * x + Renter's fee
Total Cost = $2x + $40
The total revenue for x cups is:
Total Revenue = Selling price of 1 cup * x
Total Revenue = $6x
For Akeem to break even, the total cost should be equal to the total revenue:
$2x + $40 = $6x
Rearranging the equation:
$40 = $6x - $2x
$40 = $4x
Dividing by 4:
$x = 10
Akeem needs to sell 10 cups to break even.
The total cost for x cups is:
Total Cost = Cost to make 1 cup * x + Renter's fee
Total Cost = $2x + $40
The total revenue for x cups is:
Total Revenue = Selling price of 1 cup * x
Total Revenue = $6x
For Akeem to break even, the total cost should be equal to the total revenue:
$2x + $40 = $6x
Rearranging the equation:
$40 = $6x - $2x
$40 = $4x
Dividing by 4:
$x = 10
Akeem needs to sell 10 cups to break even.
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)
• Regal Hotel: C = 75s + 1, 000; Greenhill Country Club: C = 65s + 500
• Regal Hotel: C = 1, 000s + 75; Greenhill Country Club: C = 500s + 65
• Regal Hotel: C = 500s + 75; Greenhill Country Club: C = 1,000s + 65
• Regal Hotel: C' = 75s + 500; Greenhill Country Club: C = 65s + 1, 000
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)
• Regal Hotel: C = 75s + 1, 000; Greenhill Country Club: C = 65s + 500
• Regal Hotel: C = 1, 000s + 75; Greenhill Country Club: C = 500s + 65
• Regal Hotel: C = 500s + 75; Greenhill Country Club: C = 1,000s + 65
• Regal Hotel: C' = 75s + 500; Greenhill Country Club: C = 65s + 1, 000
The correct pair of linear equations that represent this real-world problem are:
• Regal Hotel: C = 75s + 1,000; Greenhill Country Club: C = 65s + 500
• Regal Hotel: C = 75s + 1,000; Greenhill Country Club: C = 65s + 500
1 answer