Bart and Art’s ages currently are in the ratio 4 : 5. In four years, their ages will be in the ratio 9 : 11. How old are they now?

Bart is currently 32, and Art is currently 40.

Step-by-step explanation:

Step 1: Derive an Equation

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:

Step 2: Solve the Equation

Solving for , we get:

(Cross-Multiply)

(Distribute)

(Subtract and from both sides of the equation to isolate )

(Simplify / Symmetric Property of Equality)

Step 3: Answer the Question

We know that , therefore, Bart is currently years old and Art is currently years old. Hope this helps!

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