Problem:

If x varies directly as y inversely z and x is 6 when y = 3 and z = 6. Find x when y = 4 and z = 6.

Solution:

To translate into variation statement a relationship involving combined variation between two quantities.

The statement, "x varies directly as y inversely z" translated into combined variation is x = ky/z where k is the constant of variation.

Solve if x is 6 when y is 3 and z is 6. So, find the constant using the equation of a combined variation.

• x = ky/z
• (6) = k(3)/(6)
• 6 = 3k/6
• 6 × 6 = 3k
• 36/3 = 3k/3
• 12 = k

The constant of the variation is 12. In equation of variation.

• x = 12y/z

Find x when y is 4 and z is68. Substitute the equation using the constant of the variation that you obtained.

• x = 12y/z
• x = 12(4)/(6)
• x = 48/6
• x = 8

Answer:

∴ Therefore, the value of x is 8 to the combined variation.

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