To determine which system of equations accurately models the situation, let's break down the problem into manageable steps:
1. Understand the given information:
- Ashanti has been acting for \( a \) years.
- Diana has been acting for \( d \) years.
- Ashanti's acting duration is 1.5 times that of Diana's.
- Ashanti's acting duration is also 4 years longer than Diana's.
2. Translate the verbal relationships into equations:
- The first piece of information tells us that Ashanti has been acting for 1.5 times as long as Diana. This can be represented mathematically as:
[tex]\[
a = 1.5d
\][/tex]
- The second piece of information tells us that Ashanti's acting duration is 4 years longer than Diana's. This can be represented as:
[tex]\[
a = d + 4
\][/tex]
3. Combine the equations:
- We now have a system of equations:
[tex]\[
a = 1.5d
\][/tex]
[tex]\[
a = d + 4
\][/tex]
4. Choose the correct option:
- Option (A) states:
[tex]\[
a = 1.5d
\][/tex]
[tex]\[
a = d + 4
\][/tex]
- Option (B) states:
[tex]\[
a = 1.5d
\][/tex]
[tex]\[
d = a + 4
\][/tex]
- Option (C) states:
[tex]\[
d = 1.5a
\][/tex]
By examining these options, we see that option (A) represents the exact system of equations that models the relationships described in the problem. Therefore, the correct system of equations to model this situation is:
[tex]\[
\boxed{a = 1.5d}
\][/tex]
[tex]\[
\boxed{a = d + 4}
\][/tex]
Hence, the correct answer is (A).
