Question
Two students have bank accounts:
Sama: $ 43⋅ 4−4(42)−5
Jimena: $ 3 ⋅ (38)2(32)3 ⋅ 30
Which person has the most money in their account?
(1 point)
Responses
Jimena
Jimena
Sama
Sama
They have the same amount of money
They have the same amount of money
You cannot compare the total amount because the bases are different.
Sama: $ 43⋅ 4−4(42)−5
Jimena: $ 3 ⋅ (38)2(32)3 ⋅ 30
Which person has the most money in their account?
(1 point)
Responses
Jimena
Jimena
Sama
Sama
They have the same amount of money
They have the same amount of money
You cannot compare the total amount because the bases are different.
Answers
Answered by
GPT-4o mini
To determine which student, Sama or Jimena, has more money in their bank accounts, we need to calculate the dollar amounts represented by their expressions.
**Sama's amount:**
\[ 43 \cdot 4 - 4(42) - 5 \]
Calculating step-by-step:
1. \( 4(42) = 4 \times 42 = 168 \)
2. Now substitute into the expression:
\[ 43 \cdot 4 - 168 - 5 \]
3. Calculate \( 43 \cdot 4 \):
\[ 43 \cdot 4 = 172 \]
4. Now the expression is:
\[ 172 - 168 - 5 \]
5. First, subtract 168 from 172:
\[ 172 - 168 = 4 \]
6. Now, subtract 5:
\[ 4 - 5 = -1 \]
So, Sama has \(-1\) dollars.
**Jimena's amount:**
\[ 3 \cdot (38)^2 \cdot (32)^3 \cdot 30 \]
Calculating the individual components:
1. Calculate \( (38)^2 = 1444 \)
2. Calculate \( (32)^3 = 32768 \)
3. Substitute these values back:
\[ 3 \cdot 1444 \cdot 32768 \cdot 30 \]
Now calculating:
1. Calculate \( 3 \cdot 1444 = 4332 \).
2. Next, calculate:
\[ 4332 \cdot 32768 \]
This result will be quite large, but we can compute it directly.
3. Estimate \( 4332 \cdot 32768 \).
For now, if we approximate:
- \( 4332 \) is a bit less than \( 4368 \) which is \( 4352 \approx 4.3 \times 10^3 \) and \( 32768 \) is approximated as \( 3.2768 \times 10^4 \).
- The multiplication of these terms gives:
\[ 4332 \cdot 32768 \approx 143,360,000 \] (this is a rough estimate, exact calculation yields a much larger figure).
4. Finally multiply by \( 30 \):
\[ 30 \cdot 143,360,000 \approx 4,300,800,000 \].
Thus, Jimena has a very positive amount, well over 4 billion.
**Comparison:**
- Sama: \(-1\)
- Jimena: \(4,300,800,000\)
Clearly, Jimena has much more money than Sama.
**Final response:**
Jimena
**Sama's amount:**
\[ 43 \cdot 4 - 4(42) - 5 \]
Calculating step-by-step:
1. \( 4(42) = 4 \times 42 = 168 \)
2. Now substitute into the expression:
\[ 43 \cdot 4 - 168 - 5 \]
3. Calculate \( 43 \cdot 4 \):
\[ 43 \cdot 4 = 172 \]
4. Now the expression is:
\[ 172 - 168 - 5 \]
5. First, subtract 168 from 172:
\[ 172 - 168 = 4 \]
6. Now, subtract 5:
\[ 4 - 5 = -1 \]
So, Sama has \(-1\) dollars.
**Jimena's amount:**
\[ 3 \cdot (38)^2 \cdot (32)^3 \cdot 30 \]
Calculating the individual components:
1. Calculate \( (38)^2 = 1444 \)
2. Calculate \( (32)^3 = 32768 \)
3. Substitute these values back:
\[ 3 \cdot 1444 \cdot 32768 \cdot 30 \]
Now calculating:
1. Calculate \( 3 \cdot 1444 = 4332 \).
2. Next, calculate:
\[ 4332 \cdot 32768 \]
This result will be quite large, but we can compute it directly.
3. Estimate \( 4332 \cdot 32768 \).
For now, if we approximate:
- \( 4332 \) is a bit less than \( 4368 \) which is \( 4352 \approx 4.3 \times 10^3 \) and \( 32768 \) is approximated as \( 3.2768 \times 10^4 \).
- The multiplication of these terms gives:
\[ 4332 \cdot 32768 \approx 143,360,000 \] (this is a rough estimate, exact calculation yields a much larger figure).
4. Finally multiply by \( 30 \):
\[ 30 \cdot 143,360,000 \approx 4,300,800,000 \].
Thus, Jimena has a very positive amount, well over 4 billion.
**Comparison:**
- Sama: \(-1\)
- Jimena: \(4,300,800,000\)
Clearly, Jimena has much more money than Sama.
**Final response:**
Jimena