Question

Suppose 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=40

Answer 1

SOLUTION

GIVEN

• Suppose x varies directly as y and inversely as z.

• x=30 when y =40 and z=80,

TO DETERMINE

The value of x when y = 24 and z=40

EVALUATION

Here it is given that x varies directly as y and inversely as z

$\displaystyle \sf{\implies \: x \propto \: \frac{y}{z} }$

$\displaystyle \sf{\implies \: x = \: \frac{ky}{z} } \: \: \: - - - - (1)$

Where k is a non zero real number

Now x = 30 , y = 40 , z = 80 gives

$\displaystyle \sf{\implies \: 30 = \: \frac{40k}{80} } \: \: \:$

$\displaystyle \sf{\implies \:40k = 2400 } \: \: \:$

$\displaystyle \sf{\implies \:k =60 } \: \: \:$

Equation 1 gives

$\displaystyle \sf{ x = \: \frac{60y}{z} } \: \: \: - - - - (2)$

Now y = 24 , z = 40 gives

$\displaystyle \sf{\implies \: x = \: \frac{60 \times 24}{40} } \: \: \:$

$\displaystyle \sf{\implies \: x = \: 36}$

FINAL ANSWER

Hence the required value of x = 36

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