The sum of three numbers is 54. the third number is 2 times the first. the first number is 6 more than the second. what are the numbers?

Hello!

To solve this, we will use a system of equations. We will have the numbers be represented by x, y, and z, where x will represent the first, y the second, and z the third.

x+y+z=54
z=2x
x=6+y

We know that x is equal to 6+y. We can plug this into the second equation to find z.

z=12+2y

Now we can plug these y values into the first equation to find y.

6+y+y+12+2y=54
18+4y=54
4y=36
y=9

Now we know the value of y. We can plug this into the equations to find the other values.

x=6+9
x=15

z=15(2)
z=30

Just to check, we will add them all up and see if they equal 64.

15+9+30=54

The first number is 15, the second is 9, and the third is 30.

I hope this helps!