its the the number of students who rode on each bus.

Question

Stefan’s family rented a rototiller to prepare an area in their backyard for spring planting. The rental company charged an initial fee of $43 with an additional fee per hour. If they paid $64 after renting the rototiller for 7 hours, what was the hourly fee?

If h represents the hourly fee, which equation models this problem?_______

What was the hourly fee for the rototiller?_____

Answer 1

To model the problem using an equation, we can start by breaking down the total cost into its components. The total cost of renting the rototiller is made up of the initial fee plus the hourly fee multiplied by the number of hours rented.

1. Initial fee: $43
2. Hourly fee: \( h \) (this is what we are trying to find)
3. Number of hours: 7
4. Total cost: $64

We can set up the equation as follows:

\[ \text{Total Cost} = \text{Initial Fee} + (\text{Hourly Fee} \times \text{Number of Hours}) \]

Substituting the known values into the equation gives:

\[ 64 = 43 + 7h \]

Now, we can solve for the hourly fee \( h \):

1. Subtract the initial fee from both sides:

\[ 64 - 43 = 7h \]

\[ 21 = 7h \]

2. Divide both sides by 7:

\[ h = \frac{21}{7} = 3 \]

So, the hourly fee for the rototiller is $3.

Summary:

• Equation: \( 64 = 43 + 7h \)
• Hourly Fee: $3

Answer 2

okay so 1. is
7h + 43 = 64
and 2. is 3$ GOOD JOB!!

heyy Lorena solved the equation 5k – 3(2k – ) – 9 = 0. Her steps are below.

5k – 6k + 2 – 9 = 0
–k – 7 = 0
–k = 7
k =
Analyze Lorena’s work to determine which statements are correct. Check all that apply.

In Step 1, she correctly distributed –3 to the parentheses.
In Step 2, she combined like terms 5k and 2k.
In Step 3, she applied the multiplication property of equality to isolate the variable term.
In Step 4, she should have multiplied both sides by
–1 to isolate the variable.
Lorena found the correct solution to the linear equation.

Answer 3

Let's analyze each of Lorena's steps in solving the equation \(5k - 3(2k - 2) - 9 = 0\) (assuming the equation she is solving has a missing value which is likely a \(2\) instead of just a blank).

Step-by-step Analysis:

1. Step 1: \(5k - 6k + 2 - 9 = 0\)

   • Here, Lorena distributed \(-3\) correctly: \[ -3(2k - 2) = -6k + 6 \]
   • Therefore, her step should read as: \[ 5k - 6k + 6 - 9 = 0 \quad \text{(not as stated)} \]
   • Statement: Correct (about distributing \(-3\), but wrong in final simplification as she didn't properly simplify the constant terms).

2. Step 2: \(–k – 7 = 0\)

   • After distribution, combining \(5k - 6k + 6 - 9\) should yield: \[ -k - 3 = 0 \quad \text{(because } 6 - 9 = -3\text{)} \]
   • Hence, \(–k – 7 = 0\) is incorrect.
   • Statement: Incorrect (she incorrectly combined like terms).

3. Step 3: \(–k = 7\)

   • This step is actually based on the incorrect conclusion of the previous step since she didn't have \(-k - 3 = 0\).
   • So, the method of isolation used is invalid due to the error above.
   • Statement: Incorrect (she didn't apply the multiplication property of equality correctly since the previous step was incorrect).

4. Step 4: She should have multiplied both sides by \(-1\) to isolate the variable.

   • This statement is indeed correct in context. If she had ended up with \(-k = -3\) (which she should have), she would need to multiply both sides by \(-1\) to isolate \(k\).
   • Statement: Correct (in the general idea of isolating the variable).

5. Final conclusion: Lorena found the correct solution to the linear equation.

   • Since her earlier steps contained errors leading to an incorrect \(k\), this statement is incorrect.
   • Statement: Incorrect.

Summary of Correct Statements:

• In Step 1, she correctly distributed –3 to the parentheses.
• In Step 4, she should have multiplied both sides by –1 to isolate the variable.

The other statements about combining like terms, applying the multiplication property, and obtaining the correct solution were incorrect.

Answer 4

YESSS THANK YOU - **In Step 1, she correctly distributed –3 to the parentheses.**
- **In Step 4, she should have multiplied both sides by –1 to isolate the variable.**

This week, Michael collected $468 for delivering newspapers. He had 40 repeat customers and 18 new ones. As an incentive, he charged the new subscribers $3 less than the repeat customers.

If x represents the amount Michael collects from each repeat customer, which equation models this problem?_____

What is the fee Michael charges each new subscriber?____

Answer 5

Let's break down the problem step by step.

1. Variables:

   • Let \( x \) be the amount Michael collects from each repeat customer.
   • The new subscribers are charged $3 less than the repeat customers, so the fee for each new subscriber is \( x - 3 \).

2. Number of customers:

   • Michael has 40 repeat customers.
   • He has 18 new customers.

3. Total amount collected:

   • The total amount collected from repeat customers is \( 40x \).
   • The total amount collected from new subscribers is \( 18(x - 3) \).

4. Total earnings:

   • The total amount collected from both types of customers combines to equal $468: \[ 40x + 18(x - 3) = 468 \]

So, the equation that models this problem is:

\[ 40x + 18(x - 3) = 468 \]

Fee for New Subscribers:

Now, let's solve for \( x \) to determine the fee Michael charges each new subscriber.

1. Distributing: \[ 40x + 18x - 54 = 468 \]

2. Combining like terms: \[ 58x - 54 = 468 \]

3. Adding 54 to both sides: \[ 58x = 522 \]

4. Dividing by 58: \[ x = \frac{522}{58} = 9 \]

Now that we've found \( x \), which is the amount charged to each repeat customer, we can find the fee for each new subscriber:

\[ \text{Fee for new subscribers} = x - 3 = 9 - 3 = 6 \]

Summary:

• Equation: \( 40x + 18(x - 3) = 468 \)
• Fee for new subscribers: $6.

Answer 6

YOUR AWESOME 40x + 18(x - 3) = 468 and $6 THE ANSWER

Answer 7

Thank you! I'm glad you found the solution helpful! If you have any more questions or need further assistance with math or anything else, feel free to ask. Keep up the great work! 🌟