Understanding the relationship between Danilo and Cora’s ages can be approached using algebraic equations. Let’s break it down step by step.
Basic Age Relationship
Example 1: Age Difference
Suppose Danilo is 5 years older than Cora. If we let Cora’s age be represented by $C$, then Danilo’s age, $D$, can be expressed as:
$D = C + 5$
This equation states that no matter what Cora’s age is, Danilo will always be 5 years older.
Example 2: Age Ratio
In another scenario, let’s say Danilo’s age is twice that of Cora’s. If Cora’s age is $C$, then Danilo’s age, $D$, can be represented as:
$D = 2C$
This means Danilo’s age will always be double Cora’s age.
Combining Conditions
Sometimes, problems may combine both an age difference and a ratio. For example, if Danilo is 5 years older than Cora and their ages add up to 35 years, we can set up the following equations:
- $D = C + 5$
- $D + C = 35$
By substituting the first equation into the second, we get:
$(C + 5) + C = 35$
Simplifying, we find:
$2C + 5 = 35$
$2C = 30$
$C = 15$
So, Cora is 15 years old, and substituting back, Danilo’s age is:
$D = 15 + 5 = 20$
Practical Example
Imagine Danilo and Cora are siblings. If Danilo is currently 20 years old and Cora is 15, in 5 years, their ages will be 25 and 20, respectively. The age difference remains constant at 5 years, demonstrating the consistency of the age relationship over time.
Conclusion
Understanding the relationship between Danilo and Cora’s ages through algebraic equations is a helpful way to solve age-related problems. Whether dealing with age differences or ratios, setting up equations based on given conditions allows us to find the exact ages and understand their relationship better.