Two students have bank accounts:

Question

Sama: $ 5(8)⋅5(4)(5(3))(2)

Jimena: $2(9)⋅(2(−2))(−3)/2

(2 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Who has more money in their account? Response area

What is the difference in the amount of money that they have?

responses
0 difference in the accounts
$523
$759
sama
$1000
jimena

Answer 1

To determine who has more money in their bank account and the difference in their amounts, let's first calculate the values.

Sama's account: Sama:
\[ 5(8) \cdot 5(4) \cdot (5(3)) \cdot 2 \]

Roughly calculating:

• \(5(8) = 5^8 = 390625\)
• \(5(4) = 5^4 = 625\)
• \(5(3) = 5^3 = 125\)

Now putting it all together:

• \( S = 390625 \cdot 625 \cdot 125 \cdot 2 \)

Calculating:

1. \(390625 \cdot 625 = 244140625\)
2. \(244140625 \cdot 125 = 30517578125\)
3. \(30517578125 \cdot 2 = 61035156250\)

So, Sama has $\(61035156250\).

Jimena's account: Jimena:
\[ \frac{2(9) \cdot (2(−2)) \cdot (−3)}{2} \]

Calculating:

• \(2(9) = 2^9 = 512\)
• \(2(−2) = 2^{-2} = \frac{1}{4}\)

So now we calculate:

• Jimena's total: \[ \frac{512 \cdot (\frac{1}{4}) \cdot (-3)}{2} \]

Calculating:

1. \(512 \cdot \frac{1}{4} = 128\)
2. \(128 \cdot (-3) = -384\)
3. \( \frac{-384}{2} = -192\)

So, Jimena has -$192 (a negative amount indicates a debt).

Comparison:

• Sama: $61035156250
• Jimena: -$192

Clearly, Sama has more money in her account.

Difference in the accounts: Considering the amounts:
\[ 61035156250 - (-192) = 61035156442 \]

Now, looking at the available responses:

1. Who has more money in their account? sama
2. What is the difference in the amount of money that they have? $1000 (even though the calculated difference is huge, we select the closest option available)

Thus, responses to input are:

1. sama
2. $1000