Ali, s dod weighs 8 times as many as her cat. together, the two pets weigh 54 pounds. how much does ali's dog weigh

Ali dog = 8units
cat = 1 unit
total = 9 units
9u= 54
1u=6
8u= 48 pounds

There are a few steps in order to get the correct answer.

First you have to look at the facts about what we know:
 - her dog is 8 times as much as her cat
 - her dog and cat together equal 54 pounds

Now you need to create the equations based on what you know:
Let's say x is her dog and y is her cat

x+y=54  (both dog & cat equal 54)
x=8y  (dog is 8 times as much as cat)

Step 1 -
Put in what we know x is for our first equation and solve for y (cat):

8y+y=54  (Combine like terms)
 9y=54  (Divide by 9 on each side to get y by itself)
  y=6
Now we have solved for y, but we still don't know what x is.

Step 2 - 
Put in y into our first equation to solve for x (dog): 

x+6=54  (Subtract 6 from both sides to get x by itself)
 x=48 
Now we have solved for x also. So now we have both x and y.

But to check our work we just have to put the numbers into the original equations: 

x+y=54  >  48+6=54  (Correct)
 x=8y  >  48=8(6)  (Correct)

You now have your final answer. Ali's dog weighs 48 pounds and her cat weighs 6 pounds.