System of equations

We make 2 equations(x is the smaller number; y is the bigger number):

y-x=9

3x=2y

y-x=9

y=(3x)/2

(3x)/2-x=9 => (3x)/2-(2x)/2=9 => x/2=9 => x=18

y=(3*18)/2 => y=54/2 => y=27

Therefore, x and y are 18 and 27 respectively.

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The difference between two numbers is 9. Three times the smaller is equal to twice the larger.  What are the numbers? 

Let the smaller number = S

Let the larger number =L

L - S = 9 ...........(1)

3S =2L..............(2)

From (1) we have:

L = 9 + S     sub into (2)

3S = 2(9 + S)

3S = 18 + 2S

3S - 2S = 18

S = 18 the smaller number.

L - 18 = 9

L = 9 + 18

L = 27 the larger number.

too complicated!