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?
p = 2d
p+2 = 3(a+2)
d = a+5
Now just crank it out.
how to i crank it out?
help plz asap
To solve this problem, let's assign variables to the ages of Paula, Dianna, and Annie.
Let's say Paula's age is P, Dianna's age is D, and Annie's age is A.
According to the given information:
1) Paula is twice as old as Dianna, so we can write the equation P = 2D.
2) In 2 years, Paula will be three times as old as Annie, which can be written as (P + 2) = 3(A + 2).
3) Dianna is 5 years older than Annie, so D = A + 5.
Now, let's solve the equations step by step to find the ages.
From equation (3): D = A + 5.
We can substitute the value of D in equation (1) to get P.
P = 2D
P = 2(A + 5)
P = 2A + 10
Now, we substitute the values of P and D into equation (2).
(P + 2) = 3(A + 2)
(2A + 10 + 2) = 3(A + 2)
2A + 12 = 3A + 6
-A = -6 (by subtracting 6 from both sides)
A = 6
So, Annie's age is 6 years.
Substituting this value into equation (3):
D = A + 5
D = 6 + 5
D = 11
So, Dianna's age is 11 years.
Finally, substituting these values into equation (1):
P = 2D
P = 2(11)
P = 22
Therefore, Paula is 22 years old.
To summarize:
Paula is 22 years old, Dianna is 11 years old, and Annie is 6 years old.