Question


Real-World Systems of Equations Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
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Question
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=
Answer
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
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Answer
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
Answer
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
Answer
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
Answered by GPT 3.5
Equation to represent the cost at Bowl-O-Rama: C = 5g + 4

Equation to represent the cost at Bowling Pinz: C = 4g + 8
Answered by GPT 3.5
Equation to represent the total number of students: g + a = 100

Equation to represent the total cost of the gift cards: 40g + 25a = 4000
Answered by GPT 3.5
Equation for Combination 1: 4h + 2s = 10
Equation for Combination 2: 6h + 3s = 15
Answered by GPT 3.5
To determine which company is less expensive for a 300-mile trip, we need to calculate the cost for each company.

For Top-Notch Car Rental:
Total cost = $150 + $0.35/mile * 300 miles
Total cost = $150 + $105
Total cost = $255

For Fleetwood Car Rental:
Total cost = $200 + $0.10/mile * 300 miles
Total cost = $200 + $30
Total cost = $230

Therefore, Fleetwood Car Rental is less expensive for a 300-mile trip by $25.

The less expensive company is Fleetwood Car Rental by $25.
Answered by GPT 3.5
To break even, Akeem needs to make enough money to cover both his costs and the renter's fee.

Let's denote:
Cost to make one cup of lemonade = $2
Renter's fee = $40
Selling price of one cup of lemonade = $6

Let's represent the total cost (TC) and total revenue (TR) in terms of the number of cups sold (c):
TC = 2c + 40 (cost to make c cups + renter's fee)
TR = 6c (revenue from selling c cups)

For Akeem to break even, TC = TR:
2c + 40 = 6c
40 = 6c - 2c
40 = 4c
c = 40/4
c = 10

Therefore, Akeem needs to sell 10 cups of lemonade to break even.