Five times the sum of three consecutive integers is 150. what are the integers?

Alright! Let's start off with the basic from the info given:

150= 5(x+y+z)
First off, since you're looking for x y and z, let's divide both sides by 5:
30= x+y+z

Now let's change y and z written in terms of x:
y= x+1 because it's a consecutive integer
z=x+2 because it's 1 + the value for y

So let's set this up:
30= x + x+1 +x+2

Then simplify
30= 3x + 3

Since you're looking for x, let's subtract 3 then divide by 3
27= 3x
9=x

Now that you have the value of x, plug it into the equations above for y and z:
y=x+1
y= 9+1=10

z= x+2
z= 9+2 =11

Try it out!

(9+10+11) * 5 = 150
(30) * 5 = 150

150 = 150!

So you have x= 9, y= 10, and z=11

Hope this helps!