Ali currently has [tex] \$25 [/tex]. He is going to start saving [tex] \$5 [/tex] every week.

Which equation represents this situation?

A. [tex] y = 25x - 5 [/tex]
B. [tex] y = 5x + 25 [/tex]
C. [tex] y = 25x + 5 [/tex]
D. [tex] y = 5x - 25 [/tex]



Answer :

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]