Karaoke is x years old and two years older than his wife. In ten years’ time he will be 3 times as old as his daughter. What will be their total age then?
Their ages now are:
Karaoke: x
Wife: x-2
Daughter: ?
In 10 years,
Karaoke will be x+10
wife will be x-2+10=x+8
daughter: (x+10)/3
Total: (7x+64)/3
To find the total age of Karaoke, his wife, and his daughter in ten years' time, we need to determine their current ages and how they will change in the future.
Let's break down the problem step by step:
1. Let's assume Karaoke's current age is represented by "x."
2. According to the given information, Karaoke's wife is two years younger than him. Therefore, his wife's current age can be represented as "x - 2."
3. In ten years' time, Karaoke's age will be "x + 10" (since he will be 10 years older). Similarly, his wife's age will be "x - 2 + 10" or "x + 8".
4. We are also told that in ten years' time, Karaoke's age will be three times his daughter's current age. Let's assume his daughter's current age is represented by "d". Therefore, in ten years, his daughter's age will be "d + 10" (as she will be 10 years older). Thus, we can write the equation: x + 10 = 3(d + 10).
Now, let's solve the equation for d:
x + 10 = 3(d + 10)
x + 10 = 3d + 30
x = 3d + 20
Substituting this value of "x" into the expressions for Karaoke's and his wife's ages in ten years' time:
Karaoke's age = (3d + 20) + 10 = 3d + 30
Wife's age = (3d + 20) + 8 = 3d + 28
Daughter's age = d + 10
Finally, to find the total age, simply add the ages of Karaoke, his wife, and his daughter:
Total age in ten years = (3d + 30) + (3d + 28) + (d + 10) = 7d + 68
Therefore, the total age of Karaoke, his wife, and his daughter in ten years' time will be 7d + 68.