Damien is 6 years older than Emma. In 9 years the sum of their ages will be 82. How old is Damien now?
D = E + 6
D + 9 + E + 6 + 9 = 82
substituting
... (E + 6) + E + 24 = 82
Emma is X yrs. old now.
Damien is X+6 yrs. old now.
9 yrs. from now:
Emma, X+9 yrs. old.
Damien, (X+6)+9 yrs. old.
(X+9) + (X+6 + 9) = 82. X = ?.
Damien = X+6.
To determine Damien's current age, we can set up equations based on the given information.
Let's assume Damien's current age is "D" and Emma's current age is "E".
We know that Damien is 6 years older than Emma, so we can write the equation: D = E + 6.
We also know that in 9 years, the sum of their ages will be 82. So we can write another equation: (D + 9) + (E + 9) = 82.
Now, we can substitute D in the second equation with E + 6 (since D = E + 6).
(E + 6 + 9) + (E + 9) = 82.
Simplifying this equation, we get:
2E + 24 = 82.
Subtracting 24 from both sides yields:
2E = 58.
Dividing both sides by 2 gives us:
E = 29.
Now that we know Emma's age (E = 29), we can substitute this value into the first equation to find Damien's age:
D = E + 6 = 29 + 6 = 35.
Therefore, Damien is currently 35 years old.