the greater of two numbers is twelve less than twice the smaller number, and their sum is sixty.?

Let the two numbers be 'a' and 'b'.

Where (1) a+b = 60

and

(2) a = 2b - 12, i.e. assuming that a is the greater number.

So, in (1) replacing a with 2b -12 we get 2b - 12 + b = 60, which works out to be 3b - 12 = 60, i.e. 3b = 72, thus b = 72/3. b = 24

and replacing b with 24 in (2) gives a = 2(24) - 12, thus a = 48 - 12 i.e. a=36

So a = 36 (the larger number) and b = 24

Let x be the smaller number and y be the bigger. So y = 2x - 12 and x+y = 60.

Now solve these.

x + (2x-12) = 60 Which gives x = 24 and so y = 36.

Hope you can cross check!

a=36, b=24

a>b

a=2*b-12

a+b=60

a=2*b-12=>2*b-12+b=60=>3*b-12=60=>3*b=72=>b=24=>a=36

let y be geater than x

y+12 = 2x

y+x = 60

------------------

Rearrange

y - 2x = -12 (change the sign here)

y + x = 60

-----------------

after changing the sign

-y + 2x = 12

y + x = 60

----------------------

3x = 72

x = 72/3 = 24

y + 24 = 60

y = 60 - 24 = 36

answer:

x = 24

y = 36

x+y=60

x=2y-12

2y-12+y=60

3y=72

y=72/3

y=24

x=60-24

x=36