Question

Two students have bank accounts:
Sama: $ 58.54 (53) 2
Jimena: $ 29.(2-2)3 2
(2 points)
Item 10
Item 11
Item 12
Item 13
Item 14
Item 15
Who has more money in their account?
Item 16
What is the difference in the amount of money that they have?
Item 17
#$523
#$759
: 0 difference in the accounts
Jimena
Sama
$1000

Answer 1

To determine who has more money in their bank account and find the difference, we first need to understand the values of Sama's and Jimena's amounts.

1. **Sama's account**:
- The amount is given as $58.54(53)2. The notation can be interpreted with the term "53" being considered a repetitive decimal. Hence:
\[
58.54(53)2 \text{ means } 58.54 + 0.535353...
\]
To express \(0.535353...\) as a fraction, we can set:
\[
x = 0.535353...
\]
\[
100x = 53.535353...
\]
\[
100x - x = 53 \Rightarrow 99x = 53 \Rightarrow x = \frac{53}{99}
\]
Thus,
\[
Sama's total = 58.54 + \frac{53}{99}
\]

To combine \(58.54\) with \(\frac{53}{99}\), we can convert \(58.54\) to a fraction:
\[
58.54 = \frac{5854}{100} = \frac{5854 \cdot 99}{100 \cdot 99} = \frac{578346}{9900}
\]

For \(\frac{53}{99}\) to have a common denominator of \(9900\):
\[
\frac{53}{99} = \frac{53 \cdot 100}{99 \cdot 100} = \frac{5300}{9900}
\]

Therefore:
\[
Sama's total = \frac{578346 + 5300}{9900} = \frac{583646}{9900} \approx 58.876
\]

2. **Jimena's account**:
- The amount is written as \(29.(2-2)32\). The notation \( (2-2) = 0 \) indicates there is no repeating decimal, so Jimena's amount simplifies to just $29.
- Therefore:
\[
Jimena's total = 29.00
\]

3. **Comparing amounts**:
- Sama: approximately $58.876
- Jimena: $29.00

Since \(58.876\) is greater than \(29.00\), **Sama has more money in her account.**

4. **Finding the difference**:
- The difference = \(Sama's\ amount - Jimena's\ amount\):
\[
\text{Difference} = 58.54 + \frac{53}{99} - 29 = 29.54 + \frac{53}{99}
\]
We can calculate it as:
\[
= 29.54 + \frac{5300}{9900} = 29.54 + 0.535353... \approx 29.54 + 0.54 \approx 29.54 + 0.54 \approx 29.54 + 0.54 \approx 30.1
\]

Thus, the round difference would be approximately $29.54, and specifically:

- **Sama has more money in her account.**
- **The difference in their accounts is approximately $29.54.**