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.
Equation to represent the total number of students: ___ = 100
Equation to represent the total cost of the gift cards: ___ = 4,000
Let x be the number of students receiving gift cards for excellent grades and y be the number of students receiving gift cards for perfect attendance.
The total number of students is given by the equation:
x + y = 100
The total cost of the gift cards is given by the equation:
40x + 25y = 4000
Therefore, the pair of linear equations that model this situation is:
x + y = 100
40x + 25y = 4000
Both are wrong
Let \( g \) be the number of students receiving gift cards for excellent grades, and \( a \) be the number of students receiving gift cards for perfect attendance.
The total number of students is given by the equation:
\[ g + a = 100 \]
The total cost of the gift cards is given by the equation:
\[ 40g + 25a = 4000 \]
Therefore, the correct pair of linear equations that model this situation is:
\[ g + a = 100 \]
\[ 40g + 25a = 4000 \]
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.
Equation for Combination 1: ___ = 10
Equation for Combination 2: ___ = 15
Let h represent the cost of a hot dog and s represent the cost of a soda.
Combination 1 includes 4 hot dogs and 2 sodas for $10, so:
4h + 2s = 10
Combination 2 includes 6 hot dogs and 3 sodas for $15, so:
6h + 3s = 15
Therefore, the pair of linear equations that model this situation is:
4h + 2s = 10
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 $___.
For Top-Notch Car Rental, the total cost is:
\[ C_1 = 150 + 0.35m \]
For Fleetwood Car Rental, the total cost is:
\[ C_2 = 200 + 0.10m \]
For a 300-mile trip:
For Top-Notch Car Rental:
\[ C_1 = 150 + 0.35 \times 300 = 150 + 105 = 255 \]
For Fleetwood Car Rental:
\[ C_2 = 200 + 0.10 \times 300 = 200 + 30 = 230 \]
So, for a 300-mile trip, Fleetwood Car Rental is less expensive by $25.
Therefore, 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?
Let \( x \) be the number of cups Akeem sells.
The total cost for Akeem is the sum of the cost to make each cup and the rental fee:
\[ C = 2x + 40 \]
The total revenue for Akeem is the price per cup times the number of cups:
\[ R = 6x \]
To break even, the total cost equals the total revenue:
\[ 2x + 40 = 6x \]
Solving for \( x \):
\[ 40 = 6x - 2x \]
\[ 40 = 4x \]
\[ x = 10 \]
Akeem has to sell 10 cups to break even.