Ten times my age minus five times my brother's age is 100. Ten years ago square of my age plus the square of my brother's age was also 100. How old is my brother?
Ten times my age minus five times my brother's age is 100. Ten years ago square of my age plus the square of my brother's age was also 100. How old is my brother?
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Let's represent your age as x and your brother's age as y.
We have the following two equations based on the given information:
1) 10x - 5y = 100
2) (x-10)^2 + (y-10)^2 = 100
Expanding the second equation, we get:
x^2 - 20x + 100 + y^2 - 20y + 100 = 100
x^2 + y^2 - 20x - 20y + 200 = 100
x^2 + y^2 - 20x - 20y = -100
Now we can substitute the first equation into the expanded second equation:
x^2 + y^2 - 20x - 20y = -100
x^2 + y^2 - 20x - 20(2x - 20)/10 = -100 (substitute 10x - 5y = 100)
x^2 + y^2 - 20x - 4x + 40 = -100
x^2 + y^2 - 24x + 40 = -100
Rearranging the equation:
x^2 + y^2 - 24x + 40 = -100
x^2 + y^2 - 24x + 140 = 0
Now we try to find the values of x and y such that this equation is satisfied. By inspection, x = 25 and y = 20 satisfies the equation.
Therefore, your age is 25 and your brother's age is 20.