Question

Layla and Sam are both dog sitters. Layla charges $2 per day plus a sign-up fee of $3. Sam charges a flat rate of $3 per day. The system of linear equations below represents y, the total amount earned in dollars for x days of dog sitting.

1. Write the equation to represent Layla’s fees
2. Write the equation to represent Sam’s fees
3. After how many days do Layla and Sam earn the same amount for dog sitting?
What is that amount?

Answer 1

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:

$f(x)=2x+3$

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:

$g(x)=3x$

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 $f(x)=g(x)$

$2x+3=3x\\3=3x-2x\\x=3$

Therefore, on day three they are gonna earn the same amount of money.

Answer 2

Answer:

Step-by-step explanation:

Let x represent the number of days of dog sitting.

1) Layla charges $2 per day plus a sign-up fee of $3. The equation representing Layla's charges for x days of dog sitting is

y = 2x + 3

2) Sam charges a flat rate of $3 per day. The equation representing Sam's charges for x days of dog sitting is 3x.

3)for Layla and Sam to earn the same amount, the number of days would be 3 as seen from the point of intersection on the graph. The corresponding amount would be $9