Question

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?

Answer 1

Answer:

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 $4:5$, we can let their current ages be $4x$ and $5x$, respectively.

In 4 years, their ages will increase by 4. This means that in terms of $x$, Bart and Art will be $4x+4$ and $5x+4$ years old in 4 years, respectively.

We are given that their ages in 4 years will be in the ratio $9:11$. Therefore, the ratios $4x+4:5x+4$ and $9:11$ are equivalent, so $4x+4:5x+4 = 9:11$.

Ratios can also be written as fractions, so we can derive the following equation:

$\frac{4x+4}{5x+4}=\frac{9}{11}$

Step 2: Solve the Equation

Solving for $x$, we get:

$\frac{4x+4}{5x+4}=\frac{9}{11}$

$(4x+4)*11=(5x+4)*9$ (Cross-Multiply)

$44x+44=45x+36$ (Distribute)

$44x+44-44x-36=45x+36-44x-36$ (Subtract $44x$ and $36$ from both sides of the equation to isolate $x$)

$8=x \rightarrow x=8$ (Simplify / Symmetric Property of Equality)

Step 3: Answer the Question

We know that $x=8$, therefore, Bart is currently $4*8=\bf 32$ years old and Art is currently $5*8=\bf 40$ years old. Hope this helps!

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