Answer:
Givens
- Layla charges $2 per day, plus a sign-up fee of $3. Notice the sign-up fee represents a fixed value, that's gonna be the constant form of the function. And $2 is the ratio of change of the function, because it a cost per day.
- Sam charges $3 per day, without extra fee. So, the ratio of change of this function is $3, and it doesn't have a constant term.
According to the given information, the linear function for Layla is:
[tex]f(x)=2x+3[/tex]
Notice that the constant ratio of change is coefficient of the independent variable, that is, because that variable represents days, and each charges $2.
On the other hand, the linear function for Sam is:
[tex]g(x)=3x[/tex]
As we said before, this expression doesn't have any constant term, because the charges are flate $3 per day, it's just that rate.
Now, to find the number of days needed to both Layla and Sam earn the same money, we just have to solve the equation [tex]f(x)=g(x)[/tex]
[tex]2x+3=3x\\3=3x-2x\\x=3[/tex]
Therefore, on day three they are gonna earn the same amount of money.