Finding The Numbers From The Mean

Three numbers have a mean of 23.

Two of the numbers have a mean of 12.

Two of the numbers have the mean of 30.

What are the three numbers?

Since the mean of 3 numbers is 23, therefore,

23 X 3=69, but since the mean of 2 of them is 24, therefore,

69 - 24=45 must be one of the numbers, and

69-60=9 must a second number, and therefore,

69 - (45+9)=15 must the 3rd number. And so, the number are:

9, 15, 45.

Can anyone loan me their glasses please.

I definitely need different - better ones tonight  !!!    LOL     

x+y+z=69

x+y=24

y+z=60

y=(60+24-69)

y=15

x=9

z=45