Answered

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34. If z varies directly as x and inversely as y,
find the percentage change in z if x
increased by 10% and y is increased by 20%

Sagot :

AGboiiidn

Answer:

8.34%

Step-by-step explanation:

Let's assume that the constant to the proportion is 100

z varies directly as x and inversely as y

  • z = x/y

So ,

  • z = 100x / 100 y

It says , x increased by 10% and y increased by 20%

  • z = 100x + 0.1(100x) / 100y + 0.2(100)
  • z = 100x + 10x / 100y + 20y
  • z = 110x / 120y

Now , we will subtract to the original equation know the change of z

  • 100x / 100y - 110x / 120y
  • 120(100x) - 100(110x) / 1200y
  • 12000x-11000 / 12000y
  • 1000x / 12000y
  • 1x / 12y

Lastly , divide 1x /12y to the original equation to get the percentage

  • 1x / 12y ÷ x / y
  • 1x / 12y × y / x
  • 1xy / 12xy
  • 1/12
  • 0.0833

We convert 0.0833 to percent

  • 0.0833 × 100 = 8.333% or 8.34%
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