Answered

Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Get accurate and detailed answers to your questions from a dedicated community of experts on our Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

Solve the following:

[tex]\[ (+7) + (+5) = \quad (+8) + (+4) = \][/tex]

Jim is 9 years old. He is older than his sister, Kathy, by 6 years. In how many years will Jim be twice as old as Kathy?

Given:
- Jim is 9 years old.
- Kathy is 6 years younger than Jim.

Equation:
[tex]\[ 9 + x = 2(3 + x) \][/tex]

Sagot :

GinnyAnswer
Certainly! Let's break down the problem step by step to determine in how many years Jim will be twice as old as his sister Kathy.

1. Current ages:
- Jim is 9 years old.
- Kathy is 6 years younger than Jim, so Kathy is [tex]\( 9 - 6 = 3 \)[/tex] years old.

2. Future ages:
- We need to find the number of years, [tex]\( x \)[/tex], in which Jim will be twice as old as Kathy.
- In [tex]\( x \)[/tex] years, Jim’s age will be [tex]\( 9 + x \)[/tex].
- In [tex]\( x \)[/tex] years, Kathy’s age will be [tex]\( 3 + x \)[/tex].

3. Set up the equation:
- We want to find [tex]\( x \)[/tex] such that Jim is twice Kathy's age.
- This can be expressed as [tex]\( 9 + x = 2 \cdot (3 + x) \)[/tex].

4. Solve the equation:
- Start with the equation: [tex]\( 9 + x = 2 \cdot (3 + x) \)[/tex].
- Expand and simplify: [tex]\( 9 + x = 6 + 2x \)[/tex].
- Rearrange the equation to isolate [tex]\( x \)[/tex]: [tex]\( 9 - 6 = 2x - x \)[/tex].
- Simplify further: [tex]\( 3 = x \)[/tex].

So, the number of years until Jim is twice as old as Kathy is 3 years.

In summary, in 3 years, Jim will be twice as old as his sister Kathy.
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.