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:
- \( 4(42) = 4 \times 42 = 168 \)
- Now substitute into the expression: \[ 43 \cdot 4 - 168 - 5 \]
- Calculate \( 43 \cdot 4 \): \[ 43 \cdot 4 = 172 \]
- Now the expression is: \[ 172 - 168 - 5 \]
- First, subtract 168 from 172: \[ 172 - 168 = 4 \]
- 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:
- Calculate \( (38)^2 = 1444 \)
- Calculate \( (32)^3 = 32768 \)
- Substitute these values back: \[ 3 \cdot 1444 \cdot 32768 \cdot 30 \]
Now calculating:
- Calculate \( 3 \cdot 1444 = 4332 \).
- Next, calculate: \[ 4332 \cdot 32768 \] This result will be quite large, but we can compute it directly.
- 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).
- 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