The difference between two nos. is 12 and twice the larger is three times the smaller.what is the smaller no.

Let the 2 numbers be x & y

Let x be the smaller number and y the bigger number.

THE TRICK IS TO FORM 2 EQUATIONS AND SOLVE IT.

y - x = 12
y = 12 + x


2y = 3x

SUBSTITUTE FOR y

2 ( 12+x) = 3x

24 +2x = 3x
x = 24
y = 36

ANSWER = 24

Let x = the smaller number
Let y = the larger number

>> The difference between two nos. is 12 <<

y - x = 12
y = x + 12

>> twice the larger is three times the smaller <<

2y = 3x
. . . sub for y from above
2 (x + 12) = 3x
2x + 24 = 3x
x = 24 <=== the smaller number

check
y = 24 + 12 = 36
36 * 2 = 24 * 3
72 = 72

x-y=12 which is -2(x-y)=-2(12) which is -2x+2y=-24
2x=3y which is 2x-3y=0

-2x+2y=-24
2x-3y = 0
_________
-y=-24

y=24

x-y=12
x-24=12
x=12+24
x=36

The larger number is 36 and the smaller is 24.

Let x = the smaller number. x+12 = the large number
2(x+12) = 3x
x = 24 <==Answer

L-S=12
2L=3S

L=12+S
2L=3S

L=12+S
L=1.5S

12+S=1.5S

12=.5S

24=S

L-24=12

L=36

SO, LARGE IS 36, SMALL IS 24