lara is six years older than pamela. what are their present ages if in 5 years the sum of their ages is 32
Well, well, well! It seems like Lara and Pamela are on the age roller coaster! Let's see if I can assist in deciphering their ages.
Let's represent Pamela's present age as P. That means Lara's present age would be P + 6, since Lara is six years older.
Now, in five years, Pamela's age will be P + 5, and Lara's age will be P + 6 + 5, which simplifies to P + 11.
According to the information given, the sum of their ages in five years will be 32. So, we can set up an equation:
(P + 5) + (P + 11) = 32
Now, let's solve this equation for P, the mysterious age of Pamela:
2P + 16 = 32
2P = 16
P = 8
Now that we know the age of Pamela, we can calculate Lara's age. Since Pamela is 8, Lara is 8 + 6, which equals 14.
Therefore, at present, Pamela is 8 years old, and Lara is 14 years old. Time flies, huh?
Let's assume Pamela's present age as X.
According to the given information, Lara is six years older than Pamela, so Lara's age is (X + 6).
In 5 years, Pamela will be X + 5 years old, and Lara will be (X + 6) + 5 years old.
The sum of their ages in 5 years is given as 32, so we can write the equation as:
(X + 5) + ((X + 6) + 5) = 32
Simplifying the equation:
2X + 16 = 32
Subtracting 16 from both sides of the equation:
2X = 16
Dividing both sides of the equation by 2:
X = 8
So, Pamela's present age is 8 years.
Lara's present age is (8 + 6) = 14 years.
To solve this problem, let's break it down into steps:
Step 1: Define the variables.
Let's assume Pamela's current age is "x", and Lara's current age is "x + 6".
Step 2: Set up equations.
In 5 years, Pamela's age will be "x + 5", and Lara's age will be "x + 6 + 5" or "x + 11". We're given that the sum of their ages in 5 years will be 32, so we can set up the equation:
(x + 5) + (x + 11) = 32.
Step 3: Solve the equation.
Combine like terms:
2x + 16 = 32.
Subtract 16 from both sides:
2x = 16.
Divide both sides by 2:
x = 8.
Step 4: Find their present ages.
Pamela's current age is x, which we found is 8 years.
Lara's current age is x + 6, which means Lara is 8 + 6 = 14 years old.
Therefore, Pamela is 8 years old, and Lara is 14 years old.
Why use 5 and not 6?
Now:
Pam's age --- x
Lara's age --- x+5
5 years from now:
Pam is x+5
Lara is x+5 + 5 = x+10
x+5 + x+10 = 32
carry on