Question

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?

Answer 1

Now your brother is 16 and you are 18 :
1) 16×5=80;
18×10=180;
180-80=100.
Ten years ago your brother was 6 and you were 8:
2)8^2=64;
6^2=36;
64+36=100.
So your brother is 16 years old.

Answer 2

Let's assume your current age is "x" and your brother's current age is "y." We have two pieces of information from the given statements:

1. Ten times your age minus five times your brother's age is 100: 10x - 5y = 100

2. Ten years ago, the square of your age plus the square of your brother's age was also 100: (x - 10)^2 + (y - 10)^2 = 100

Now, let's solve the system of equations to find the values of "x" and "y."

Step 1: Solve the first equation for "x": 10x - 5y = 100 10x = 100 + 5y x = (100 + 5y) / 10 x = 10 + 0.5y

Step 2: Substitute the expression for "x" from Step 1 into the second equation: (10 + 0.5y - 10)^2 + (y - 10)^2 = 100 (0.5y)^2 + (y - 10)^2 = 100 0.25y^2 + (y - 10)^2 = 100

Step 3: Expand the equation and bring all terms to one side: 0.25y^2 + y^2 - 20y + 100 - 100 = 0 1.25y^2 - 20y = 0

Step 4: Factor out common terms: y(1.25y - 20) = 0

Step 5: Set each factor to zero and solve for "y": y = 0 or 1.25y - 20 = 0

If y = 0, it would imply that your brother's age is zero, which is not reasonable. So, let's proceed with solving for "y" in the second equation:

1.25y - 20 = 0 1.25y = 20 y = 20 / 1.25 y = 16

So, your brother's current age is 16 years old. Now, to find your age (x), we can use the equation we derived earlier:

x = 10 + 0.5y x = 10 + 0.5(16) x = 10 + 8 x = 18

Therefore, your current age is 18 years old, and your brother's current age is 16 years old.