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 AA, BB, and CC respectively. We are given the following information:

  1. After 10 years, Ajay will be two times as old as Bhushan is today. A+10=2BA + 10 = 2B Rearranging, we get: A=2B10A = 2B - 10

  2. Five years ago, Chandru was younger than Bhushan by 10 years. C5=B510C - 5 = B - 5 - 10 Simplifying, we get: C=B10C = B - 10

  3. After 5 years, Ajay will be seven times as old as Chandru was five years ago. A+5=7(C5)A + 5 = 7(C - 5) Substituting C=B10C = B - 10 into the equation: A+5=7(B105)A + 5 = 7(B - 10 - 5) Simplifying: A+5=7(B15)A + 5 = 7(B - 15) Expanding and simplifying further: A+5=7B105A + 5 = 7B - 105 A=7B110A = 7B - 110

Step 1: Solve the system of equations

We now have two equations involving AA and BB:

  1. A=2B10A = 2B - 10
  2. A=7B110A = 7B - 110

Equating the two expressions for AA: 2B10=7B1102B - 10 = 7B - 110 Subtract 2B2B from both sides: 10=5B110-10 = 5B - 110 Add 110 to both sides: 100=5B100 = 5B Divide by 5: B=20B = 20

Step 2: Calculate AA and CC

Using B=20B = 20 in the equation A=2B10A = 2B - 10: A=2(20)10=4010=30A = 2(20) - 10 = 40 - 10 = 30

Using B=20B = 20 in the equation C=B10C = B - 10: C=2010=10C = 20 - 10 = 10

Step 3: Find the sum of their ages

The sum of the current ages of Ajay, Bhushan, and Chandru is: A+B+C=30+20+10=60A + B + C = 30 + 20 + 10 = 60

Thus, the sum of their current ages is 60 years.

Would you like more details or have any questions? Here are some related questions:

  1. What other methods could be used to solve this problem?
  2. How can we verify that the solution is correct?
  3. What if the conditions were slightly different? How would that change the solution?
  4. How do you solve problems with more than three variables?
  5. 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.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Linear equations
Age problems

Formulas

Equations involving ages

Theorems

-

Suitable Grade Level

Grades 7-9