Reann has stickers. She gives her friend half, and then her brother gives her 8 new ones. She ends up with 12 stickers. How many did she start with? Identify the operations needed to solve this problem

Answer 1

To find out how many stickers Reann started with, let's denote the number of stickers she initially had as \( x \).

According to the problem:

1. Reann gives half of her stickers to her friend, which means she has \( \frac{x}{2} \) stickers left.
2. Then, her brother gives her 8 new stickers, so she now has: \[ \frac{x}{2} + 8 \]
3. We know that after these transactions, she ends up with 12 stickers. We can set up the equation: \[ \frac{x}{2} + 8 = 12 \]

Now, let's solve the equation step by step:

1. Subtract 8 from both sides: \[ \frac{x}{2} = 12 - 8 \] \[ \frac{x}{2} = 4 \]

2. Multiply both sides by 2 to solve for \( x \): \[ x = 4 \times 2 \] \[ x = 8 \]

Therefore, Reann started with 8 stickers.

Summary of Operations to Solve the Problem:

• Identify the half operation: Giving half of the stickers.
• Addition: When her brother gives her 8 stickers.
• Set up an equation: Combine the results and set it equal to 12.
• Algebraic manipulation: Solving the equation step by step (subtracting and multiplying).

Answer 2

addition and multiplication
addition and multiplication

addition and division
addition and division

subtraction and multiplication
subtraction and multiplication

subtraction and division

Answer 3

Based on the context of the original problem involving Reann's stickers, let's clarify the operations involved in solving it:

1. Identify Operations: Initially, Reann gives away half her stickers, receives some back, and then we set this equal to her final count.

Here are the operations we performed:

• Division: When Reann gives away half her stickers (i.e., calculating \( \frac{x}{2} \)).
• Addition: When her brother gives her 8 stickers (i.e., adding 8 to her remaining stickers).
• Subtraction: When we subtracted 8 from 12 to isolate \( \frac{x}{2} \).

Given this, the specific operations used in solving the problem were:

• Division (to calculate half of her stickers),
• Addition (to factor in the 8 stickers received),
• Subtraction (to rearrange the equation before solving for \( x \)),
• Multiplication (to solve for \( x \) after simplifying).

Summary of Correct Sequences:

• First operation (for half): Division
• Second operation (for receiving 8): Addition
• Third operation (subtracting): Subtraction
• Fourth operation (to find the starting count): Multiplication

So if we're to match operations to the context given in your options:

• Division and addition (used to find out how many stickers she had after giving away half and adding the 8 received).
• Subtraction and multiplication (used to solve the equation).

You can group or list the operations like this:

• Addition and Division (related to receiving and halving)
• Subtraction and Multiplication (related to isolating \( x \) in the equation)

If you're looking for a specific pair of operations to list based on your given options, it would be:

• Addition and Division
• Subtraction and Multiplication

I hope this clarifies the operations involved!

Answer 4

You can only choose one answer

Answer 5

Given the problem and the operations used to solve it, the best choice from your options would be:

Subtraction and Multiplication

This choice reflects the final steps we used to solve the equation after isolating the sticker count, specifically:

1. Subtraction (to isolate the variable, subtracting 8 from both sides).
2. Multiplication (to solve for \( x \) by multiplying both sides by 2).

So, Subtraction and Multiplication is the appropriate answer based on the context of the problem.

Answer 6

How did you come to this answer

Answer 7

To arrive at the answer Subtraction and Multiplication, I reviewed the steps involved in solving the original problem about Reann's stickers. Here is a breakdown of the reasoning process:

1. Problem Statement Recap:

   • Reann gives half of her stickers to a friend, then receives 8 new stickers from her brother, and ends up with 12 stickers.

2. Setting Up the Equation:

   • Let \( x \) represent the number of stickers Reann started with.
   • After giving half away, she has \( \frac{x}{2} \).
   • After receiving 8 stickers, her total is given by the equation: \[ \frac{x}{2} + 8 = 12 \]

3. Solving the Equation:

   • To isolate \( \frac{x}{2} \), we first subtract 8 from both sides: \[ \frac{x}{2} = 12 - 8 \] \[ \frac{x}{2} = 4 \]
   • Next, we need to eliminate the fraction by multiplying both sides by 2: \[ x = 4 \times 2 \] \[ x = 8 \]

4. Identifying the Operations:

   • The steps used to solve the equation involved:
     • Subtraction: When we subtracted 8 from both sides to isolate \( \frac{x}{2} \).
     • Multiplication: When we multiplied both sides by 2 to solve for \( x \).

Summary of Choice:

Since the single steps that directly contributed to solving for \( x \) were the subtraction (to isolate the variable) and the multiplication (to find the original number of stickers), I concluded that the answer is Subtraction and Multiplication.

This combination is the most relevant to the final steps taken after forming the equation based on the problem.

Answer 8

Sam is buying packages with 9 beads each. His mom bought him 63 more beads. Now, he has 153 beads. How many packages did he buy? Use algebra to determine the answer

Answer 9

To solve for the number of packages Sam bought, let's define the variables and set up the equation step by step.

1. Define the Variables:

   • Let \( p \) be the number of packages Sam bought.
   • Since each package contains 9 beads, the total number of beads Sam bought is \( 9p \).

2. Understand the Problem:

   • Sam's mom bought him 63 additional beads.
   • After his mom's purchase, Sam has a total of 153 beads.

3. Set Up the Equation:

   • The total beads Sam has can be expressed as: \[ 9p + 63 = 153 \]

4. Solve the Equation:

   • First, subtract 63 from both sides: \[ 9p = 153 - 63 \] \[ 9p = 90 \]
   • Next, divide both sides by 9 to solve for \( p \): \[ p = \frac{90}{9} \] \[ p = 10 \]

Thus, Sam bought 10 packages of beads.

Answer 10

Triana is on a 120-mile four-day bike ride. On the first day she travels 24 miles. She would like to travel equal amounts over the remaining three days. How far will she travel on each of those three days? Write and solve an equation of the form px+q=r . Then write a sentence to explain your answer

Answer 11

To find out how far Triana will travel on each of the remaining three days of her bike ride, we can set up an equation based on the information provided.

Step 1: Define Variables

Let \( x \) be the distance Triana will travel each day for the remaining three days.

Step 2: Set Up the Equation

Triana has already traveled 24 miles on the first day. The total distance for the entire trip is 120 miles, so the distance she needs to cover over the next three days can be expressed as:

\[ 24 + 3x = 120 \]

Here, \( 3x \) represents the total distance traveled over the last three days.

Step 3: Rearranging the Equation

To write this in the form \( px + q = r \), we can rearrange it:

\[ 3x + 24 = 120 \]

This equation fits the form where:

• \( p = 3 \)
• \( q = 24 \)
• \( r = 120 \)

Step 4: Solve the Equation

Now, we can solve for \( x \):

1. Subtract 24 from both sides: \[ 3x = 120 - 24 \] \[ 3x = 96 \]

2. Divide both sides by 3: \[ x = \frac{96}{3} \] \[ x = 32 \]

Conclusion

Triana will travel 32 miles on each of the remaining three days.

Summary Sentence

Triana will travel 32 miles each day for the next three days to complete her 120-mile bike ride, after already covering 24 miles on the first day.