To determine the month when Felix will have enough money to completely pay for his motorcycle, we need to set up two equations:
1. The first equation will represent his total savings over time, including his initial savings and the extra amount he saves each month.
2. The second equation will represent the remaining cost of the motorcycle, considering the monthly payments he makes.
Starting with Felix's savings:
- Felix initially has [tex]$1,000$[/tex].
- He saves an extra [tex]$300$[/tex] each month.
So, the equation for his savings over time (in terms of months [tex]\(x\)[/tex]) will be:
[tex]\[ y = 300x + 1,000 \][/tex]
Next, considering the cost of the motorcycle:
- The motorcycle initially costs [tex]$5,000$[/tex].
- Felix makes a [tex]$250$[/tex] payment each month.
The equation representing the remaining cost of the motorcycle (in terms of months [tex]\(x\)[/tex]) will be:
[tex]\[ y = 5,000 - 250x \][/tex]
Now, we have the system of equations:
[tex]\[ y = 300x + 1,000 \][/tex]
[tex]\[ y = 5,000 - 250x \][/tex]
Comparing these with the given options, the correct answer is:
C. [tex]\( y = 300x + 1,000 \)[/tex]
[tex]\[ y = 5,000 - 250x \][/tex]
