SOLUTION: A list contains 11 consecutive integers. If x is the smallest integer and y is the greatest integer on the list, and 16x^-2=y^-2. Find the value of (x+y)?

Algebra ->  Equations -> SOLUTION: A list contains 11 consecutive integers. If x is the smallest integer and y is the greatest integer on the list, and 16x^-2=y^-2. Find the value of (x+y)?      Log On


   

Question 662445: A list contains 11 consecutive integers. If x is the smallest integer and y is the greatest integer on the list, and 16x^-2=y^-2. Find the value of (x+y)?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
The list of 11 consists of

1.  x
2.  x+1
3.  x+2
4.  x+3
5.  x+4
6.  x+5
7.  x+6
8.  x+7
9.  x+8
10. x+9
11. x+10

So x is the the smallest and y = x+10 is the largest.

16x-2 = y-2

Using the definition of negative exponents:

16%2Fx%5E2 = 1%2Fy%5E2

Cross-multiply

16y² = x²

Since y = x+10, substitute x+10 for y

16(x+10)² = x²

Solve that for x, then find y from y = x+10, 

Then it'll be easy to find (x+y)

If you have trouble, you may ask me in the thank-you note.

Edwin