The sum of two numbers is 20. The difference between three times the first number and twice the second is 40. Find the two numbers.

Their sum can be written as : a+b=20. this means that b=20-a

and the phrase: The difference between three times the first number and twice the second is 40 like this:

3a-2b=40

and we can substitute:

3a-2b=40

3a-2 (20-a) = 40

3a-40+2a=40

5a=40+40

5a=80

a=16

so b must be 4!

let's check:

3*16-2*4=48-8=40 correct!