Ask a New Question
Menu

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

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

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

Jimena
Jimena

Sama

1 answer

To determine who has more money in their account, we need to simplify both expressions.

Sama's Amount: \[ Sama: 43 \cdot 4 - 4(42) - 5 \] This expression can be calculated step by step:

  1. Calculate \( 4(42) \): \[ 4(42) = 4 \cdot 42 = 168 \]

  2. Now substitute that back into the expression: \[ 43 \cdot 4 - 168 - 5 \]

  3. Calculate \( 43 \cdot 4 \): \[ 43 \cdot 4 = 172 \]

  4. Substitute again: \[ 172 - 168 - 5 \]

  5. Now calculate \( 172 - 168 \): \[ 172 - 168 = 4 \]

  6. Finally, subtract 5: \[ 4 - 5 = -1 \]

So, Sama's amount is \(-1\) dollars.

Jimena's Amount: \[ Jimena: 3 \cdot (38)^2 \cdot (32)^3 \cdot 30 \] Let's break this down. First, we need to calculate each element:

  1. Calculate \( (38)^2 \): \[ (38)^2 = 1444 \]

  2. Calculate \( (32)^3 \): \[ (32)^3 = 32768 \]

  3. Now substitute these values back into the expression: \[ Jimena: 3 \cdot 1444 \cdot 32768 \cdot 30 \]

  4. Let's first calculate: \[ 3 \cdot 1444 = 4332 \]

  5. Now, multiply \( 4332 \) by \( 32768 \): \[ 4332 \cdot 32768 = 1427485696 \]

  6. Finally, multiply that result by \( 30 \): \[ 1427485696 \cdot 30 = 42824570880 \]

So, Jimena's amount is \( 42824570880 \) dollars.

Comparison:

  • Sama: \(-1\) dollars
  • Jimena: \(42824570880\) dollars

Based on the calculations, Jimena has significantly more money in her account compared to Sama.

Final Answer: Jimena.