Let's break down the problem step by step to find the correct equation that represents Ali's savings over time.
1. Current Savings:
Ali starts with an initial amount of money, which is [tex]$25. This represents his starting point or his initial savings.
2. Weekly Savings:
Each week, Ali saves an additional $[/tex]5. This means that for every week that passes, the amount of money Ali saves increases linearly.
Let's denote:
- [tex]\( y \)[/tex] as the total amount of money Ali has after a certain number of weeks.
- [tex]\( x \)[/tex] as the number of weeks that have passed.
3. Deriving the Equation:
- Initially (when [tex]\( x = 0 \)[/tex]), Ali has [tex]$25, which can be written as \( y = 25 \).
- For each additional week (\( x \)), Ali saves $[/tex]5. Thus, the total amount of money Ali has after [tex]\( x \)[/tex] weeks can be expressed as the sum of his initial savings and his weekly savings multiplied by the number of weeks.
The formula to express this relationship is:
[tex]\[ y = \text{initial savings} + \text{weekly savings} \times x \][/tex]
Plugging in the values we have:
[tex]\[ y = 25 + 5x \][/tex]
So, the equation that represents Ali's savings after [tex]\( x \)[/tex] weeks is:
[tex]\[ y = 5x + 25 \][/tex]
4. Choosing the Correct Option:
From the options given:
- [tex]\( y = 25x - 5 \)[/tex]
- [tex]\( y = 5x + 25 \)[/tex]
- [tex]\( y = 25x + 5 \)[/tex]
- [tex]\( y = 5x - 25 \)[/tex]
The correct equation that matches our derived formula is:
[tex]\[ y = 5x + 25 \][/tex]
Therefore, the correct choice is:
2) [tex]\( y = 5x + 25 \)[/tex]
