Question 29765
Let the first number be x
Let the second number be y
x-y=12
y=-12+x (subsitution)


Greater number 2x/5
Lesser number = 1y/3


Equation:
{{{2x/5=6+1y/3}}}
Multiply the whole equation by 15 to remove the fraction.
{{{15(2x/5)=15(6/1)+15(1y/3)}}}
{{{3(2x)=15(6)+5(y)}}}
{{{6x=90+5y}}}
Subsitute
6x=90+5(-12+x)
6x=90-60+5x
x=30

y=-12+30
y=18


Check:
{{{(2(30))/5=6+18/3}}}
12=12


<font color = green>Hence, the two numbers are 30 and 18</font>
Paul.