In 5 years, Ana's age will be twice the age of her friend Jun. 5 years ago, she was 3 times as old as her friend. Find their present ages.
Anna's present age -- x
Jun's present age ---- y
in 5 yrs form now:
Anna --- x+5
Jun ----- y+5
x+5 = 2(y+5)
x+5 = 2y + 10
x - 2y = 5
5 years ago:
Anna --- x-5
jun ----- y-5
x-5 = 3(y-5)
x-5 = 3y - 15
x - 3y = -10
subtract the two equations:
y = 15
then in x - 2y=5
x - 30 = 5
x = 35
Anna is now 35 , her friend jun is now 15
check:
5 years from now, Anna will be 40, Jun will be 20
Anna will be twice as old as Jun
5 yrs ago, Anna was 30 and Jun was 10
Anna was 3 times as old as Jun
My answer is correct
How did you get Y=15
Cause when you less the 2 equation, the answer will be 1. Correct me if I'm wrong please.
Let's assign variables to represent the present ages of Ana and Jun.
Let A be Ana's present age.
Let J be Jun's present age.
According to the given information, in 5 years, Ana's age will be twice the age of Jun:
A + 5 = 2(J + 5) [Equation 1]
Also, 5 years ago, Ana was 3 times as old as Jun:
A - 5 = 3(J - 5) [Equation 2]
To solve this system of equations, we can start by simplifying Equation 1:
A + 5 = 2J + 10
A = 2J + 10 - 5
A = 2J + 5 [Equation 3]
Then, we can substitute Equation 3 into Equation 2:
2J + 5 - 5 = 3(J - 5)
2J = 3J - 15
2J - 3J = -15
-J = -15
J = 15
Now that we know Jun's present age is 15, we can substitute this value back into Equation 3 to find Ana's present age:
A = 2(15) + 5
A = 30 + 5
A = 35
Therefore, Ana's present age is 35 and Jun's present age is 15.
To solve this problem, we can use a system of equations. Let's represent Ana's current age as A, and Jun's current age as J.
From the given information, we can write two equations:
Equation 1: In 5 years, Ana's age will be twice Jun's age.
A + 5 = 2(J + 5)
Equation 2: 5 years ago, Ana was 3 times Jun's age.
A - 5 = 3(J - 5)
Now, we can solve this system of equations to find the values of A and J.
From Equation 1, expand the equation:
A + 5 = 2J + 10
Simplify it:
A = 2J + 10 - 5
A = 2J + 5 Equation 3
Now, substitute Equation 3 into Equation 2:
2J + 5 - 5 = 3(J - 5)
Simplify it:
2J = 3J - 15
Rearrange the equation by subtracting 2J from both sides:
2J - 3J = -15
Simplify it further:
-J = -15
Divide both sides by -1:
J = 15
Now substitute J = 15 into Equation 3:
A = 2(15) + 5
A = 30 + 5
A = 35
So, Ana's present age is 35, and Jun's present age is 15.