Write an equation which models how old in years each of you will be when you are three times as old as the younger person. My age is 30, my son is 6.
30+x=3(6+x)
first observe that you are 24 years older than your son. also, since we are required of the ages, we represent these unknown ages using variables:
let x = your son's age
let x+24 = your age
note that when your son's age is x years, you are three times as old. therefore,
3x = x+24
3x-x = 24
2x = 24
x = 12 years old (age of your son)
and your age is
x+24 = 36 years old
checking: note that 12*3 = 36, which satisfies the condition given.
hope this helps~ :)
To model the ages, we need to create a system of equations. Let's assume "x" represents the number of years from now, when both of you will be three times as old as the younger person.
Given that your current age is 30 and your son's current age is 6, we can add "x" years to each of your ages to model the future ages.
Your age in "x" years will be 30 + x.
Your son's age in "x" years will be 6 + x.
Based on the problem, we know that you will be three times as old as your son in "x" years:
30 + x = 3(6 + x)
This equation states that your future age in "x" years will be three times your son's future age in "x" years.
Now, let's solve the equation to find the value of "x".
Expanding the equation:
30 + x = 18 + 3x
Combining like terms:
x - 3x = 18 - 30
-2x = -12
Dividing both sides by -2:
x = (-12) / (-2)
x = 6
Therefore, "x" represents 6 years from now.
To find the ages after 6 years, substitute the value of "x" back into the equation:
Your age after 6 years:
30 + x = 30 + 6 = 36
Your son's age after 6 years:
6 + x = 6 + 6 = 12
Hence, in 6 years, you will be 36 years old, and your son will be 12 years old.