The total ages of Sweta, Damini and Supriya is 56 years. What was the total of their ages 3 years ago?
47 years
Calculate Total Ages Years Ago
Let the current ages of Sweta, Damini, and Supriya be \(S\), \(D\), and \(P\) respectively.
According to the question, the total of their current ages is 56 years.
So, we have the equation:
\(S + D + P = 56\) years
We need to find the total of their ages 3 years ago.
3 years ago, the age of Sweta was \(S - 3\) years.
3 years ago, the age of Damini was \(D - 3\) years.
3 years ago, the age of Supriya was \(P - 3\) years.
The total of their ages 3 years ago would be the sum of their individual ages at that time.
Total ages 3 years ago = \((S - 3) + (D - 3) + (P - 3)\)
Let's simplify this expression:
Total ages 3 years ago = \(S - 3 + D - 3 + P - 3\)
Group the age variables and the numbers:
Total ages 3 years ago = \((S + D + P) - (3 + 3 + 3)\)
Total ages 3 years ago = \((S + D + P) - 9\)
We already know that the current total age, \(S + D + P\), is 56 years.
Substitute the current total age into the equation:
Total ages 3 years ago = \(56 - 9\)
Now, perform the subtraction:
\(56 - 9 = 47\)
So, the total of their ages 3 years ago was 47 years.
Step-by-Step Calculation of Total Ages
- Identify the current total age: 56 years.
- Identify the number of people: 3 (Sweta, Damini, Supriya).
- Identify the time period in the past: 3 years ago.
- For each person, their age 3 years ago was their current age minus 3 years.
- Since there are 3 people, the total reduction in their combined age over 3 years is \(3 \times 3 = 9\) years.
- Subtract this total reduction from the current total age to find the total age 3 years ago.
- Calculation: \(56 - 9 = 47\).
Summarizing the Age Calculation
| Description | Value |
|---|---|
| Current Total Age | 56 years |
| Number of People | 3 |
| Years Ago | 3 years |
| Total Age Reduction (\(3 \times 3\)) | 9 years |
| Total Age 3 Years Ago (\(56 - 9\)) | 47 years |
Therefore, the total of their ages 3 years ago was 47 years.
Revision Table: Understanding Age Problems
| Concept | Explanation | How it applies here |
|---|---|---|
| Current Age | A person's age at the present time. | Sum of current ages of Sweta, Damini, Supriya is 56. |
| Past Age | A person's age at a point in time before the present. Calculated by subtracting the number of years from the current age. | Age of each person 3 years ago is their current age minus 3. |
| Total Age | The sum of the ages of a group of people. | Current total age is 56. We calculated the total age 3 years ago. |
| Change in Total Age | When calculating total age for a past or future time, the change is the number of people multiplied by the number of years. | 3 people * 3 years = 9 years reduction in total age. |
Additional Information: Age Calculations and Word Problems
Age-related problems are common in mathematics, often involving calculating ages at different points in time (past or future) or finding relationships between the ages of different people.
- Individual Age Change: If you want to find a person's age \(N\) years ago, you subtract \(N\) from their current age. If you want to find their age \(N\) years from now, you add \(N\) to their current age.
- Group Total Age Change: When dealing with a group of \(M\) people over a period of \(N\) years, the total age of the group changes by \(M \times N\) years.
- Total age \(N\) years ago = Current total age - \((M \times N)\)
- Total age \(N\) years from now = Current total age + \((M \times N)\)
- Setting up Equations: For more complex problems involving relationships between ages (e.g., "A is twice as old as B"), assign variables to the unknown ages and set up algebraic equations based on the given information. Solve the equations to find the ages.
Understanding how the total age of a group changes over time is key to solving problems like the one presented, where the individual ages are not known, but the total age is given.
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