SOLUTION: Suppose that y varies inversely as x^2 and z varies directly as x^2. When x = 2, y + z = 340; when x = 1, y − z = 1275. For what values of x is y = z?

Algebra ->  Finance -> SOLUTION: Suppose that y varies inversely as x^2 and z varies directly as x^2. When x = 2, y + z = 340; when x = 1, y − z = 1275. For what values of x is y = z?      Log On


   

Question 1150726: Suppose that y varies inversely as x^2 and z varies directly as x^2. When x = 2, y + z = 340; when x = 1, y − z = 1275. For what values of x is y = z?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


y+=+a%2Fx%5E2 a is the constant of variation
z+=+bx%5E2 b is the constant of variation

x=2: a%2F4%2B4b+=+340

x=1: a%2F1-1b+=+1275

Multiply the first equation by 4 and subtract the second equation to eliminate a and solve for b.
   a+16b = 1360
   a- 1b = 1275
  --------------
     17b = 85

b = 5

Substitute into the first equation and solve for a.
a/4+4(5) = 340
a/4 = 320
a = 1280

y = z:

a%2Fx%5E2+=+bx%5E2
1280%2Fx%5E2+=+5x%5E2
256+=+x%5E4
x=4 or x=-4

ANSWER: x = 4 or x = -4