Math Problem Statement
After 10 years, Ajay will be two times as old as Bhushan is today. Five years ago, Chandru was younger than Bhushan by 10 years. After 5 years, Ajay will be seven times as old as Chandru was five years ago. What is the sum of the current ages of Ajay, Bhushan and Chandru? (All ages are in years)
Solution
Let's define the current ages of Ajay, Bhushan, and Chandru as , , and respectively. We are given the following information:
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After 10 years, Ajay will be two times as old as Bhushan is today. Rearranging, we get:
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Five years ago, Chandru was younger than Bhushan by 10 years. Simplifying, we get:
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After 5 years, Ajay will be seven times as old as Chandru was five years ago. Substituting into the equation: Simplifying: Expanding and simplifying further:
Step 1: Solve the system of equations
We now have two equations involving and :
Equating the two expressions for : Subtract from both sides: Add 110 to both sides: Divide by 5:
Step 2: Calculate and
Using in the equation :
Using in the equation :
Step 3: Find the sum of their ages
The sum of the current ages of Ajay, Bhushan, and Chandru is:
Thus, the sum of their current ages is 60 years.
Would you like more details or have any questions? Here are some related questions:
- What other methods could be used to solve this problem?
- How can we verify that the solution is correct?
- What if the conditions were slightly different? How would that change the solution?
- How do you solve problems with more than three variables?
- Why is it important to check the consistency of your equations?
Tip: When solving word problems, breaking down the problem step by step and translating the words into equations can help make the problem more manageable.
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Math Problem Analysis
Mathematical Concepts
Linear equations
Age problems
Formulas
Equations involving ages
Theorems
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Suitable Grade Level
Grades 7-9
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