What is the solution to this system of equations?Your combined table for both companies is below:

Question

Kites Purchased: 0,1,4,7,10
Total Cost for Kites-R-Fun: $10,$16,$22,$28,$34
Total Cost for Windy Kites:$16,$20,$24,$28,$32

Answer 1

To find the solution to the system of equations given the total costs for Kites-R-Fun and Windy Kites, we can first establish the relationship between the kites purchased and their respective total costs.

Data Summary

For Kites-R-Fun:

• Kites Purchased: 0, 1, 4, 7, 10
• Total Cost: $10, $16, $22, $28, $34

For Windy Kites:

• Kites Purchased: 0, 1, 4, 7, 10
• Total Cost: $16, $20, $24, $28, $32

Determine Cost Per Kite

We can deduce the cost per kite for each company by finding the slope (cost increase per kite) from their total costs.

For Kites-R-Fun:

1. Calculate the cost per kite:

   • From the first two points (0, $10) and (1, $16):

     • Increase in total cost = $16 - $10 = $6
     • Increase in kites = 1 - 0 = 1
     • Cost per kite = $6 / 1 = $6

   • This pattern continues, so the cost per kite for Kites-R-Fun is consistent at $6.

For Windy Kites:

1. Calculate the cost per kite:

   • From the first two points (0, $16) and (1, $20):

     • Increase in total cost = $20 - $16 = $4
     • Increase in kites = 1 - 0 = 1
     • Cost per kite = $4 / 1 = $4

   • This pattern is consistent as well, and the cost per kite for Windy Kites seems to be $4.

Formulating the Equations

Now we can write the equations for each company based on the total costs:

• Let \(x\) be the number of kites purchased.

Kites-R-Fun: \[ C_{R-F} = 10 + 6x \] Where \(C_{R-F}\) is the total cost for Kites-R-Fun.

Windy Kites: \[ C_{W} = 16 + 4x \] Where \(C_{W}\) is the total cost for Windy Kites.

Finding the Solution to the System

To find when the costs are equal, we set the two equations equal to each other.

\[ 10 + 6x = 16 + 4x \]

Now, solve for \(x\):

1. Rearranging the terms: \[ 6x - 4x = 16 - 10 \] \[ 2x = 6 \] \[ x = 3 \]

Determine the Total Costs

Now plug \(x = 3\) back into either total cost equation to find the respective total cost.

Using Kites-R-Fun: \[ C_{R-F} = 10 + 6(3) = 10 + 18 = 28 \]

Using Windy Kites: \[ C_{W} = 16 + 4(3) = 16 + 12 = 28 \]

Conclusion

The solution of the system is that when 3 kites are purchased, both companies charge a total cost of $28.

Answer 2

so what is the answer? your wrong.

Answer 3

Let's reassess the situation based on the provided data to ensure that we accurately determine the relationship between the number of kites purchased and the total cost for each company.

Given Data

Kites-R-Fun:

• Kites Purchased: 0, 1, 4, 7, 10
• Total Cost: $10, $16, $22, $28, $34

Windy Kites:

• Kites Purchased: 0, 1, 4, 7, 10
• Total Cost: $16, $20, $24, $28, $32

Finding the Cost Per Kite

1. Calculate the coefficients for Kites-R-Fun:

   \[ \text{Cost per kite for Kites-R-Fun} = \frac{\text{Change in total cost}}{\text{Change in kites purchased}} \]

   • From $10 to $16 (0 to 1 kite):
     • Increase in cost: $16 - $10 = $6 for 1 kite.
   • From $16 to $22 (1 to 4 kites):
     • Increase over 3 kites: $22 - $16 = $6.
   • From $22 to $28 (4 to 7 kites):
     • Increase over 3 kites: $28 - $22 = $6.
   • From $28 to $34 (7 to 10 kites):
     • Increase over 3 kites: $34 - $28 = $6.

   Thus, the pattern holds, cost per kite is $6, with a fixed start cost of $10.

   The equation for Kites-R-Fun can be written as: \[ C_{R-F} = 10 + 6x \]

2. Calculate the coefficients for Windy Kites:

   • From $16 to $20 (0 to 1 kite):
     • Increase in cost: $20 - $16 = $4 for 1 kite.
   • From $20 to $24 (1 to 4 kites):
     • Increase over 3 kites: $24 - $20 = $4.
   • From $24 to $28 (4 to 7 kites):
     • Increase over 3 kites: $28 - $24 = $4.
   • From $28 to $32 (7 to 10 kites):
     • Increase over 3 kites: $32 - $28 = $4.

   Thus, the cost per kite for Windy Kites is $4 with a starting cost of $16.

   The equation can be written as: \[ C_{W} = 16 + 4x \]

Setting the Total Costs Equal

Now we set the two equations equal to find when the costs are the same:

\[ 10 + 6x = 16 + 4x \]

Solving for \(x\)

1. Rearranging: \[ 6x - 4x = 16 - 10 \] \[ 2x = 6 \] \[ x = 3 \]

Confirming the Total Costs at \(x = 3\)

1. Kites-R-Fun: \[ C_{R-F} = 10 + 6(3) = 10 + 18 = 28 \]

2. Windy Kites: \[ C_{W} = 16 + 4(3) = 16 + 12 = 28 \]

So, when 3 kites are purchased, both companies charge a total of $28.

Final Answer

The answer is that when 3 kites are purchased, the total cost for both companies is $28. If there's a specific aspect of the question I may have misunderstood or if there was an error in interpretation, please let me know so I can assist you accurately.

Answer 4

What is the solution to this system of equations?

Answer 5

To solve the system of equations based on the data given for Kites-R-Fun and Windy Kites, let's summarize everything clearly and then analyze the setup.

Given Data

• Kites-R-Fun:

  • Kites Purchased: 0, 1, 4, 7, 10
  • Total Cost: $10, $16, $22, $28, $34

• Windy Kites:

  • Kites Purchased: 0, 1, 4, 7, 10
  • Total Cost: $16, $20, $24, $28, $32

Step 1: Formulating the Equations

We can derive the equations for total cost based on the data provided.

Kites-R-Fun:

• We can see that the cost increases by $6 for each kite:
  • Cost formula: \( C_{R-F} = 10 + 6x \)
  • This means the cost starts at $10 (for 0 kites) and increases by $6 for each additional kite.

Windy Kites:

• The cost increases by $4 for each kite:
  • Cost formula: \( C_{W} = 16 + 4x \)
  • The starting cost is $16 (for 0 kites), increasing by $4 for each additional kite.

Step 2: Setting the Equations Equal

To find out when both companies' costs are the same, we set \( C_{R-F} \) equal to \( C_{W} \):

\[ 10 + 6x = 16 + 4x \]

Step 3: Solving for \(x\)

1. Rearranging the equation:

   \[ 6x - 4x = 16 - 10 \]

   \[ 2x = 6 \]

   \[ x = 3 \]

Step 4: Calculate Total Cost at \(x = 3\)

Now, let’s find the total costs for both companies when \(x = 3\):

For Kites-R-Fun:

\[ C_{R-F} = 10 + 6(3) = 10 + 18 = 28 \]

For Windy Kites:

\[ C_{W} = 16 + 4(3) = 16 + 12 = 28 \]

Conclusion

The solution to the system of equations shows that when 3 kites are purchased, both companies will charge a total of $28.

If this is not the information you were seeking, please clarify, and I would be glad to help further!

Answer 6

give me an equation

Answer 7

Certainly! Based on the data provided for Kites-R-Fun and Windy Kites, here are the equations for the total cost based on the number of kites purchased.

Kites-R-Fun Equation

The total cost \(C_{R-F}\) for Kites-R-Fun can be written as: \[ C_{R-F} = 10 + 6x \] Where:

• \(C_{R-F}\) is the total cost for Kites-R-Fun.
• \(x\) is the number of kites purchased.

Windy Kites Equation

The total cost \(C_{W}\) for Windy Kites can be written as: \[ C_{W} = 16 + 4x \] Where:

• \(C_{W}\) is the total cost for Windy Kites.
• \(x\) is the number of kites purchased.

Summary of the Equations

So, the equations you can use to represent the total costs are:

1. Kites-R-Fun: \[ C_{R-F} = 10 + 6x \]

2. Windy Kites: \[ C_{W} = 16 + 4x \]

If you have any other specific requests or need further clarification, feel free to ask!