Certainly! Let's solve the given system of equations step-by-step and understand the meaning of the number 380 in the context:
We are given two equations:
1. \( r = 1.5t \)
2. \( r - t = 380 \)
Where:
- \( r \) is the number of followers Rossana has.
- \( t \) is the number of followers Ty has.
We want to find the values of \( r \) and \( t \).
### Step 1: Substitute \( r \) from the first equation into the second equation
From the first equation, we know that \( r = 1.5t \). We can substitute this value into the second equation to eliminate \( r \):
[tex]\[
r - t = 380 \quad \Rightarrow \quad 1.5t - t = 380
\][/tex]
### Step 2: Simplify and solve for \( t \)
Now, combine the terms involving \( t \):
[tex]\[
0.5t = 380
\][/tex]
To isolate \( t \), divide both sides by 0.5:
[tex]\[
t = \frac{380}{0.5} = 760
\][/tex]
So, Ty has 760 followers.
### Step 3: Find \( r \) using the value of \( t \)
Now that we have the value of \( t \), we can substitute it back into the first equation to find \( r \):
[tex]\[
r = 1.5t = 1.5 \times 760 = 1140
\][/tex]
Thus, Rossana has 1140 followers.
### Step 4: Understanding the number 380
The number 380 represents the difference in the number of followers between Rossana and Ty. Specifically, Rossana has 380 more followers than Ty. This can be verified by the second equation:
[tex]\[
r - t = 1140 - 760 = 380
\][/tex]
In summary:
- Rossana has 1140 followers.
- Ty has 760 followers.
- The number 380 is the difference between Rossana's and Ty's followers. Rossana has 380 more followers than Ty.
