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X varies directly as y and inversely as z. If x=30 when y=40 and z=80, find x when y=24 and z=60.

Sagot :

SOLUTION

First, finding the constant of the variation

[tex]x = \frac{ky}{z} \\ 30 = \frac{k(40)}{80} \\ {40} = \frac{k}{2} \\ 40(2) = k \\ 80 = k[/tex]

Then , finding for the unknown variable to a given condition

[tex]x = \frac{ky}{z} \\ x = \frac {24(80)}{60} \\ x = \frac{24(4)}{3} \\ x = \frac{\cancel{24} \: ^{8} (4)}{ \cancel {3} \: ^{1} } \\ x = 8(4) \\ x = 32[/tex]

ANSWER

  • x = 32

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