The difference of 2 numbers is 12. 2 fifths of the greater # is 6 more than 1 third of the lesser #.?

Question

The difference of 2 numbers is 12. 2 fifths of the greater # is 6 more than 1 third of the lesser #. Find both numbers.
I NEED HELP, PLZ ANSWER!!!

Answer 1

Two variables, so you need 2 equations.
"The difference of 2 numbers is 12" becomes: x-y=12 (x is going to be the greater number)

"2 fifths of the greater # is 6 more than 1 third of the lesser #." becomes two fifths of x = one third y +6
or 2/5x= 1/3y+6.

So, your two equations are:
x-y=12
2/5x= 1/3y+6

Now use the 1st equation to define x as x=12+y (we added y to each side of the equation.)

Substitute this in to the 2nd equation:
2/5(12+y)= 1/3y+6
24/5 + 2/5y = 1/3y +6
24+2y = 5/3y + 30
24+1/3y = 30
1/3y = 6
y=18

If y =18, then x = 30. (based on that 1st equation)

Answer 2

Just write the two things you know in equation form.

Let the two numbers be x and y such that x > y:
x - y = 12
2/5*x = 6 + 1/3*y

Now solve the system of equations by substitution to get:
x = 30
y = 18