Answer:
Bart is currently 32, and Art is currently 40.
Step-by-step explanation:
<u>Step 1: Derive an Equation</u>
Since Bart and Art's current ages are in a ratio of , we can let their current ages be
and
, respectively.
In 4 years, their ages will increase by 4. This means that in terms of , Bart and Art will be
and
years old in 4 years, respectively.
We are given that their ages in 4 years will be in the ratio . Therefore, the ratios
and
are equivalent, so
.
Ratios can also be written as fractions, so we can derive the following equation:
<u>Step 2: Solve the Equation</u>
Solving for , we get:
(Cross-Multiply)
(Distribute)
(Subtract
and
from both sides of the equation to isolate
)
(Simplify / Symmetric Property of Equality)
<u>Step 3: Answer the Question</u>
We know that , therefore, Bart is currently
years old and Art is currently
years old. Hope this helps!
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