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?

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) (Show Source): You can put this solution on YOUR website!

a is the constant of variation
b is the constant of variation

x=2:

x=1:

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:

or

ANSWER: x = 4 or x = -4

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