Janet is twice as old as Doug, while Peter is 5 years older than Doug. If their ages are added the answer is 95 years. Use algebra to calculate the age of each of them.
explain any assumptions made, demonstrate all reasoning and show full working out
j = 2d
p = d+5
j+d+p = 95
Now just solve for the ages
Let's break down the problem step by step.
Let's assume Doug's age as x.
According to the problem, Janet is twice as old as Doug. Therefore, Janet's age would be 2x.
Additionally, Peter is 5 years older than Doug. Hence, Peter's age would be x + 5.
According to the problem, if their ages are added, the answer is 95 years.
So, we can write an equation to represent this:
x + 2x + (x + 5) = 95
Now, let's solve this equation to find the value of x (Doug's age).
Combining like terms, we have:
4x + 5 = 95
Subtracting 5 from both sides:
4x = 90
Dividing both sides by 4, we get:
x = 22.5
Now we have found Doug's age, which is 22.5 years.
To find Janet's age (twice that of Doug's), we can substitute the value of x back into the equation:
Janet's age = 2 * Doug's age = 2 * 22.5 = 45 years.
Lastly, to find Peter's age (5 years older than Doug's), we can substitute the value of x back into the equation:
Peter's age = Doug's age + 5 = 22.5 + 5 = 27.5 years.
Therefore, Doug is 22.5 years old, Janet is 45 years old, and Peter is 27.5 years old.