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)

Question

Equation to represent the cost at Bowl-O-Rama: C=

Equation to represent the cost at Bowling Pinz: C=

Answer 1

To represent the cost at each bowling alley, you can write the equations based on the information provided.

1. For Bowl-O-Rama, the cost \( C \) is defined by the number of games \( g \) multiplied by the cost per game ($5) plus the shoe rental cost ($4). The equation is:

\[ C = 5g + 4 \]

2. For Bowling Pinz, the cost \( C \) is defined by the number of games \( g \) multiplied by the cost per game ($4) plus the shoe rental cost ($8). The equation is:

\[ C = 4g + 8 \]

So the pair of linear equations that model this situation is:

1. For Bowl-O-Rama: \( C = 5g + 4 \)
2. For Bowling Pinz: \( C = 4g + 8 \)

Answer 2

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

Answer 3

To model the situation described with the equations, let \( g \) represent the number of gift cards awarded for excellent grades and \( a \) represent the number of gift cards awarded for perfect attendance.

1. The first equation represents the total number of students being recognized, which is 100:

\[ g + a = 100 \]

2. The second equation represents the total cost of the gift cards. Each gift card for excellent grades is worth $40, and each gift card for perfect attendance is worth $25. The total cost must equal $4,000:

\[ 40g + 25a = 4000 \]

Thus, the pair of linear equations that model this situation is:

1. Total number of students: \( g + a = 100 \)
2. Total cost of the gift cards: \( 40g + 25a = 4000 \)

Answer 4

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 5

To model the situation with the combinations sold at the concession stand, we can set up the equations based on the given information.

1. For Combination 1, which includes 4 hot dogs and 2 sodas for $10, the equation can be written as:

\[ 4h + 2s = 10 \]

2. For Combination 2, which includes 6 hot dogs and 3 sodas for $15, the equation can be written as:

\[ 6h + 3s = 15 \]

Thus, the pair of linear equations that model this situation is:

1. Combination 1: \( 4h + 2s = 10 \)
2. Combination 2: \( 6h + 3s = 15 \)

Answer 6

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 7

To determine which car rental company is less expensive for a 300-mile trip, we can calculate the total cost \( C \) for both companies.

Top-Notch Car Rental

For Top-Notch, the total cost can be calculated as follows: \[ C = 150 + 0.35m \] If \( m = 300 \) miles, then: \[ C = 150 + 0.35(300) = 150 + 105 = 255 \]

Fleetwood Car Rental

For Fleetwood, the total cost can be calculated as follows: \[ C = 200 + 0.10m \] If \( m = 300 \) miles, then: \[ C = 200 + 0.10(300) = 200 + 30 = 230 \]

Comparison

Now we compare the total costs:

• Top-Notch Car Rental: $255
• Fleetwood Car Rental: $230

Fleetwood Car Rental is less expensive.

Difference in Cost

To find out by how much: \[ \text{Difference} = 255 - 230 = 25 \]

Final Answer

The less expensive company is 2 by $25.

Answer 8

The booster club is selling refreshments. The following system of linear equations models the concession stand prices. Let represent the cost of a hot dog and represent the cost of the soda. Write the answers in decimal form. Solve the system of linear equations.

4h+4s=10


7h+5s=15


(1 point)
h=$

s=$

Answer 9

To solve the system of linear equations given by:

1. \( 4h + 4s = 10 \)
2. \( 7h + 5s = 15 \)

we will solve for \( h \) (the cost of a hot dog) and \( s \) (the cost of a soda) step-by-step.

Step 1: Simplify the first equation

The first equation can be simplified by dividing everything by 4:

\[ h + s = 2.5 \quad \text{(Equation 1)} \]

Step 2: Solve Equation 1 for \( s \)

We can express \( s \) in terms of \( h \):

\[ s = 2.5 - h \quad \text{(Substitute this into the second equation)} \]

Step 3: Substitute \( s \) in the second equation

Now substitute \( s \) into the second equation \( 7h + 5s = 15 \):

\[ 7h + 5(2.5 - h) = 15 \]

Step 4: Distribute and solve for \( h \)

Distributing the 5:

\[ 7h + 12.5 - 5h = 15 \]

Combine like terms:

\[ (7h - 5h) + 12.5 = 15 \]

\[ 2h + 12.5 = 15 \]

Step 5: Isolate \( h \)

Subtract 12.5 from both sides:

\[ 2h = 15 - 12.5 \]

\[ 2h = 2.5 \]

Now divide by 2:

\[ h = \frac{2.5}{2} = 1.25 \]

Step 6: Substitute \( h \) back to find \( s \)

Now use the value of \( h \) to find \( s \):

\[ s = 2.5 - h = 2.5 - 1.25 = 1.25 \]

Conclusion

The solutions are:

\[ h = 1.25 \quad (cost , of , a , hot , dog) \]

\[ s = 1.25 \quad (cost , of , a , soda) \]

Final Answer

• \( h = $1.25 \)
• \( s = $1.25 \)

Answer 10

bot is 100% correct

Answer 11

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