The sum of their current ages is 18 years
Let the age of Billy be x
Let the age of his brother be y
If billy is 1/5 of his brother's age, then x = 1/5 y
In 9 years time,
Billy's age = x + 9
Her brother age = y + 9
If in 9 years, billy will be 1/2 of his brother's age, then;
x + 9 = 1/2(y+9)
2(x+9) = y + 9
Recall that x = 1/5 y
y = 5x
The expression above becomes
2(x+9)=5x+9
2x+18 = 5x+9
2x - 5x = 9- 18
-3x = -9
x = 3
Since y = 5x
y = 5(3)
y = 15
The sum of their current ages = x + y = 3 + 15 = 18 years
Hence the sum of their current ages is 18 years
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