Answered

Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Experience the convenience of getting reliable answers to your questions from a vast network of knowledgeable experts. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

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?

Sagot :

snog

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 [tex]4:5[/tex], we can let their current ages be [tex]4x[/tex] and [tex]5x[/tex], respectively.

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

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

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

[tex]\frac{4x+4}{5x+4}=\frac{9}{11}[/tex]

Step 2: Solve the Equation

Solving for [tex]x[/tex], we get:

[tex]\frac{4x+4}{5x+4}=\frac{9}{11}[/tex]

[tex](4x+4)*11=(5x+4)*9[/tex] (Cross-Multiply)

[tex]44x+44=45x+36[/tex] (Distribute)

[tex]44x+44-44x-36=45x+36-44x-36[/tex] (Subtract [tex]44x[/tex] and [tex]36[/tex] from both sides of the equation to isolate [tex]x[/tex])

[tex]8=x \rightarrow x=8[/tex] (Simplify / Symmetric Property of Equality)

Step 3: Answer the Question

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

To learn more about these types of problems, check out the following questions:

https://brainly.com/question/7808200

https://brainly.com/question/23126206

Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.