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

They have the same amount of money
They have the same amount of money

Jimena
Jimena

You cannot compare the total amount because the bases are different.
You cannot compare the total amount because the bases are different.

Sama
Sama

Answer 1

To compare the amounts in Sama's and Jimena's bank accounts, we first need to simplify the expressions for each student's account.

**Sama's Amount:**
\[
43 \cdot 4 - 4(42) - 5
\]
Calculating this step by step:
1. \( 4(42) = 4 \cdot 4^2 = 4 \cdot 16 = 64 \)
2. Now substitute this back into the expression:
\[
43 \cdot 4 - 64 - 5
\]
3. Calculate \( 43 \cdot 4 = 172 \).
4. Now plug it in:
\[
172 - 64 - 5 = 172 - 69 = 103
\]

So, Sama has $103.

**Jimena's Amount:**
\[
3 \cdot (38)^2 \cdot (32)^3 \cdot 30
\]
Calculating each part:
1. \( (38)^2 = 1444 \)
2. \( (32)^3 = 32 \cdot 32 \cdot 32 = 1024 \cdot 32 = 32768 \)
3. Now we calculate:
\[
3 \cdot 1444 \cdot 32768 \cdot 30
\]
4. This expression is quite large, but we can estimate or calculate as follows:
- First calculate \( 3 \cdot 1444 = 4332 \)
- Now we have:
\[
4332 \cdot 32768 \cdot 30
\]
- Multiply \( 32768 \cdot 30 = 983040 \)
- Then, finally multiply \( 4332 \cdot 983040 \) which will be a large number.

Calculating that gives us a much larger figure than 103.

In conclusion, Jimena has the most money in her account.

Thus the answer is:
**Jimena**