Three numbers have an average of 14. the smallest number is six less than the middle number and the largest number is four less than twice the middle number. use an algebraic model to find all three numbers.

Let x(largest), y(middle) and z(smallest) be the 3 numbers.
According to your question: z=y-3 and ×=2y-4

Because we know the average we'd do the following: (x+y+z)/3=14 (add all the three numbers and divide them by 3)

Now just substitute
[(2y-4)+y+(y-3)]/3=14
Now simplify
2y+y+y=4y
-4-3=-7
You get [4y-7]/3=14
Now multiply both sides by 3
4y-7=42
Now add 7 to both sides
4y=49
Now divide both sides by 4
y=49/4(middle number)
Substitute y in z and x
z= (49/4)-3 = 37/4(smallest)
x=2 (49/4)-4 = 41/2(largest)

Those are the three numbers
To check your work substitute x,y and z in the first equation, you will get 14

First, think of what you know. you know that the number t the end of the equation will need to be subtracted because it is the money he lost from buying the lawn mower. and your first two weeks have negative profit, so that tells you that c and d are wrong. now you can plug any of the weeks into a and b to see which one works. i'll start with plugging week 1 into a.this isn't right because it says your answer for week one should be -90.so now we need to try the same thing with b.this one got you the right answer, (sometimes if you only check with one of the weeks multiple will work so you need to check with more of the weeks, but it worked out fine here)this means that b is the correct answer.let me know if you need more clarification. i hope this : )