Question
One of your classmates was absent on the day that you learned how to write and solve an equation from a contextual situation. Your teacher has asked you to explain the four steps and their application to the problem that follows.
Natasha stole three fewer bases than twice the number Elena stole. If Natasha stole 15 bases, how many did Elena steal?
Using the four steps from this lesson, write and solve an equation to find the number of bases Elena stole.
Natasha stole three fewer bases than twice the number Elena stole. If Natasha stole 15 bases, how many did Elena steal?
Using the four steps from this lesson, write and solve an equation to find the number of bases Elena stole.
Answers
GPT-4o mini
To help your classmate understand how to write and solve an equation based on the given contextual situation, you can use the four steps:
### Step 1: Understand the problem
First, we need to clarify the information given in the problem. We know:
- Natasha stole 15 bases.
- Natasha stole three fewer bases than twice the number Elena stole.
Let’s denote the number of bases that Elena stole as \( E \).
### Step 2: Set up the equation
From the information, we can write an equation based on the statement "Natasha stole three fewer bases than twice the number Elena stole." This can be expressed mathematically as:
\[
N = 2E - 3
\]
Where:
- \( N \) is the number of bases Natasha stole (which is 15),
- \( E \) is the number of bases Elena stole.
Substituting the value for \( N \):
\[
15 = 2E - 3
\]
### Step 3: Solve the equation
Now we need to solve for \( E \).
1. Start by adding 3 to both sides of the equation:
\[
15 + 3 = 2E
\]
\[
18 = 2E
\]
2. Next, divide both sides by 2 to isolate \( E \):
\[
E = \frac{18}{2}
\]
\[
E = 9
\]
### Step 4: Check the solution
Finally, we should check our solution to ensure it makes sense in the context of the problem. If Elena stole 9 bases, then we need to verify that Natasha stole three fewer bases than twice that amount:
- Twice the number of bases Elena stole is \( 2 \times 9 = 18 \),
- Three fewer bases than that is \( 18 - 3 = 15 \).
Since Natasha stole 15 bases, our solution is correct.
### Conclusion
So, Elena stole **9 bases**.
Your classmate can follow these four steps to understand how to derive equations from contextual situations and find solutions accurately.
### Step 1: Understand the problem
First, we need to clarify the information given in the problem. We know:
- Natasha stole 15 bases.
- Natasha stole three fewer bases than twice the number Elena stole.
Let’s denote the number of bases that Elena stole as \( E \).
### Step 2: Set up the equation
From the information, we can write an equation based on the statement "Natasha stole three fewer bases than twice the number Elena stole." This can be expressed mathematically as:
\[
N = 2E - 3
\]
Where:
- \( N \) is the number of bases Natasha stole (which is 15),
- \( E \) is the number of bases Elena stole.
Substituting the value for \( N \):
\[
15 = 2E - 3
\]
### Step 3: Solve the equation
Now we need to solve for \( E \).
1. Start by adding 3 to both sides of the equation:
\[
15 + 3 = 2E
\]
\[
18 = 2E
\]
2. Next, divide both sides by 2 to isolate \( E \):
\[
E = \frac{18}{2}
\]
\[
E = 9
\]
### Step 4: Check the solution
Finally, we should check our solution to ensure it makes sense in the context of the problem. If Elena stole 9 bases, then we need to verify that Natasha stole three fewer bases than twice that amount:
- Twice the number of bases Elena stole is \( 2 \times 9 = 18 \),
- Three fewer bases than that is \( 18 - 3 = 15 \).
Since Natasha stole 15 bases, our solution is correct.
### Conclusion
So, Elena stole **9 bases**.
Your classmate can follow these four steps to understand how to derive equations from contextual situations and find solutions accurately.
can you make this less advanced
GPT-4o mini
Sure! Let's simplify the explanation of how to solve the problem with easier language and concepts.
### Step 1: Understand the Problem
We need to figure out how many bases Elena stole based on the information about Natasha. Here’s what we know:
- Natasha stole **15 bases**.
- Natasha stole **three fewer than twice** what Elena stole.
Let's call the number of bases Elena stole **E**.
### Step 2: Write an Equation
We can write an equation based on what we know. The sentence "Natasha stole three fewer than twice the number Elena stole" means:
- **Twice** Elena's bases: \( 2E \)
- Then, **three fewer** means we subtract 3: \( 2E - 3 \)
Now, since we know Natasha stole 15 bases, we can set up the equation:
\[
15 = 2E - 3
\]
### Step 3: Solve the Equation
Now, we need to find out what \( E \) is. Here’s how to do it step by step:
1. Start with the equation:
\[
15 = 2E - 3
\]
2. Add 3 to both sides to get rid of the -3:
\[
15 + 3 = 2E
\]
\[
18 = 2E
\]
3. Now, divide both sides by 2 to solve for \( E \):
\[
E = \frac{18}{2}
\]
\[
E = 9
\]
### Step 4: Check the Solution
Let’s double-check our answer to make sure it’s correct:
If Elena stole **9 bases**, then:
- Twice the number of bases Elena stole is \( 2 \times 9 = 18 \).
- Three fewer than this would be \( 18 - 3 = 15 \).
That matches what Natasha stole (15 bases), so our answer is correct!
### Conclusion
Elena stole **9 bases**.
Now you can share this simple breakdown with your classmate!
### Step 1: Understand the Problem
We need to figure out how many bases Elena stole based on the information about Natasha. Here’s what we know:
- Natasha stole **15 bases**.
- Natasha stole **three fewer than twice** what Elena stole.
Let's call the number of bases Elena stole **E**.
### Step 2: Write an Equation
We can write an equation based on what we know. The sentence "Natasha stole three fewer than twice the number Elena stole" means:
- **Twice** Elena's bases: \( 2E \)
- Then, **three fewer** means we subtract 3: \( 2E - 3 \)
Now, since we know Natasha stole 15 bases, we can set up the equation:
\[
15 = 2E - 3
\]
### Step 3: Solve the Equation
Now, we need to find out what \( E \) is. Here’s how to do it step by step:
1. Start with the equation:
\[
15 = 2E - 3
\]
2. Add 3 to both sides to get rid of the -3:
\[
15 + 3 = 2E
\]
\[
18 = 2E
\]
3. Now, divide both sides by 2 to solve for \( E \):
\[
E = \frac{18}{2}
\]
\[
E = 9
\]
### Step 4: Check the Solution
Let’s double-check our answer to make sure it’s correct:
If Elena stole **9 bases**, then:
- Twice the number of bases Elena stole is \( 2 \times 9 = 18 \).
- Three fewer than this would be \( 18 - 3 = 15 \).
That matches what Natasha stole (15 bases), so our answer is correct!
### Conclusion
Elena stole **9 bases**.
Now you can share this simple breakdown with your classmate!
can you use just a little bit less words
GPT-4o mini
Of course! Here’s a more concise version:
### Step 1: Understand the Problem
- Natasha stole **15 bases**.
- Natasha stole **three fewer than twice** what Elena stole.
- Let’s call the number of bases Elena stole **E**.
### Step 2: Write the Equation
From the information, we can set up the equation:
\[
15 = 2E - 3
\]
### Step 3: Solve the Equation
1. Add 3 to both sides:
\[
15 + 3 = 2E \quad \Rightarrow \quad 18 = 2E
\]
2. Divide by 2:
\[
E = \frac{18}{2} \quad \Rightarrow \quad E = 9
\]
### Step 4: Check the Solution
- If Elena stole **9 bases**:
- Twice that is \( 2 \times 9 = 18 \).
- Three fewer is \( 18 - 3 = 15\).
This matches Natasha's bases.
### Conclusion
Elena stole **9 bases**.
This is a clear step-by-step explanation that should be easy to follow!
### Step 1: Understand the Problem
- Natasha stole **15 bases**.
- Natasha stole **three fewer than twice** what Elena stole.
- Let’s call the number of bases Elena stole **E**.
### Step 2: Write the Equation
From the information, we can set up the equation:
\[
15 = 2E - 3
\]
### Step 3: Solve the Equation
1. Add 3 to both sides:
\[
15 + 3 = 2E \quad \Rightarrow \quad 18 = 2E
\]
2. Divide by 2:
\[
E = \frac{18}{2} \quad \Rightarrow \quad E = 9
\]
### Step 4: Check the Solution
- If Elena stole **9 bases**:
- Twice that is \( 2 \times 9 = 18 \).
- Three fewer is \( 18 - 3 = 15\).
This matches Natasha's bases.
### Conclusion
Elena stole **9 bases**.
This is a clear step-by-step explanation that should be easy to follow!