Funny riddle

Riddle me this???? herb

(x+y)/2 - c = z
x - c = y
2z - c = x

2z - c = y + c
2z - 2c = y
z - c = y/2
{(x+y)/2 - c} - c = y/2
(x+y)/2 - 2c = y/2
x + y - 4c = y
x = 4c

4c - c = y
y = 3c

Yeah, the sister is 4/3s as old as the brother

2z - c = 4c
2z = 5c
z = 5/2c

(x+y)/2 - 5/2c = c
x + y - 5c = 2c
x + y = 7c

Yep, all consistent. c=x/4

x = 16
y = 12

(12+16)/2 - (16-12) = z
14 - 4 = 10
2(10) - 4 = 16
20 - 4 = 16

x = 12
y = 9

(12+9)/2 - 3 = z
10.5 - 3 = 7.5
15 - 3 = 12

I don't understand any of that shit in brackets, but I worked out the difference between their ages.

Originally posted by lord xyz
(x+y)/2 - c = z
x - c = y
2z - c = x

2z - c = y + c
2z - 2c = y
z - c = y/2
{(x+y)/2 - c} - c = y/2
(x+y)/2 - 2c = y/2
x + y - 4c = y
x = 4c

4c - c = y
y = 3c

Yeah, the sister is 4/3s as old as the brother

2z - c = 4c
2z = 5c
z = 5/2c

(x+y)/2 - 5/2c = c
x + y - 5c = 2c
x + y = 7c

Yep, all consistent. c=x/4

x = 16
y = 12

(12+16)/2 - (16-12) = z
14 - 4 = 10
2(10) - 4 = 16
20 - 4 = 16

x = 12
y = 9

(12+9)/2 - 3 = z
10.5 - 3 = 7.5
15 - 3 = 12

I don't understand any of that shit in brackets, but I worked out the difference between their ages.

A mother is half as old as her son will be when the mother's age is twice the sum of the age of the mother and the son when the mother was as old as the son currently is.

Mother's current age: x
Son's current age: y
Difference between ages: c

Mother's future age: 2x+c
Son's future age: 2x
Mother's past age: z+c
Son's past age: z

z+c=y
2(2z+c)=2x+c
c=x-y

2(2(y-c)+c)=2x+c
2(2y-2c+c)=2x+c
4y-4c+2c=2x+c
4y-2c=2x+c
4y=2x+3c
4y=2x+3(x-y)
4y=2x+3x-3y
7y=5x
y=5/7x

Son is 5/7s the age of his mother.

x-y=c
x-(5/7)x=c
2/7x=c

x=35
y=25
c=10
z=25-10=15

2(2z+c)=2x+c
2(2(15)+10)=2(35)+10
2(30+10)=17+10
2(40)=80

😉

Or simply:

It's virtually the same thing. But it's less messy to solve with matrix algebra and you can even recreate similar problems like I just did without having to spend a lot of time on it.

I do not understand Matrix Algebra.

Although you are right, simultaneous equations are a real *****.

Originally posted by lord xyz
I do not understand Matrix Algebra.

Although you are right, simultaneous equations are a real *****.

Say you have three equations.

x + y - z
2x - 3z
3y

You'd write that:

1 1 -1
2 0 -3
0 3 0

Then you subtract or add lines with one another until you get something like.

1 0 0
0 1 0
0 0 1

In which case that would be translated to

x =
y =
z =