Paula, Dianna and Annie are three friends. Paula is twice as old as Dianna, and in 2 years she will be three times as old as Annie. If Dianna is 5 years older than Annie, how old is Paula?
To solve this problem, we can use a system of equations.
Let's denote Paula's age as P, Dianna's age as D, and Annie's age as A.
From the given information, we have three equations:
1. Paula is twice as old as Dianna: P = 2D
2. In 2 years, Paula will be three times as old as Annie: P + 2 = 3(A + 2)
3. Dianna is 5 years older than Annie: D = A + 5
Now we can substitute the values in equation 3 into equations 1 and 2.
From equation 3, we can rewrite it as A = D - 5.
Substituting A = D - 5 into equation 1, we get P = 2(D - 5), which simplifies to P = 2D - 10.
Substituting A = D - 5 into equation 2, we get P + 2 = 3((D - 5) + 2), which simplifies to P + 2 = 3D - 9.
Now we can substitute the value of P from equation 1 into equation 2:
2D - 10 + 2 = 3D - 9
Simplifying further, we get 2D - 8 = 3D - 9.
Subtracting 2D from both sides, we get -8 = D - 9.
Now, adding 9 to both sides, we get 1 = D.
So, Dianna is 1 year old.
From equation 3, we can find Annie's age: A = D - 5 = 1 - 5 = -4.
Since Annie's age cannot be negative, there seems to be a mistake or inconsistency in the information provided about the ages of the three friends. Please double-check the information given or provide additional information to find the age of Paula accurately.
P=2D
P+2=3(A+2)
D-5=A
Does that help?