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If 150 were increased by 60% and then decreased by y%, the result would be 192. What is the value of y?

My solution is to use percent change. Here are my steps and yet my answer is incorrect. Can someone please advise why my answer is incorrect? Thanks.

  1. $150 * 0.60 = 90$
  2. $150 + 90 = 240$
  3. Percent change = ((New value − Old value) /Old value) $∗ 100$
  4. New value = $240$, Old Value = $192$
  5. $((240-192)/192)*100 = 25$
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    $\begingroup$ You say to divide by the old value, but you are using 192, which is the new value. The new value is 192, while the old value is 240. $\endgroup$
    – Peanut
    Jun 30 '20 at 20:18
  • $\begingroup$ The correct answer is 20%, as you can check by plugging the correct values $\endgroup$
    – Peanut
    Jun 30 '20 at 20:21
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"Increasing by 60%" is multiplying by $1.60$.

"Decreasing by $y$%" is mutiplying by $1-\tfrac{y}{100}$.

You know that $150(1.60)(1-\tfrac{y}{100}) = 192$.

So, solving for $y$, the desired percentage is $y = 100\left(1 - \dfrac{192}{150(1.60)}\right) = \boxed{20}$.

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to increase by 60% you multiply by 1,6 so you get 240 wich you did to decrease bei y% yo u multiply by 1-y/100 so you have 240*(1-y/100)=192 1-(y/100)=192/240=0.8 so y is 0.2*100=20 your kind of reasoning 240-192=48 but 240 is the old value, 192 the new, and 48 is 20% of 240 or 48/240=0.2=20%

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    $\begingroup$ This is almost impossible to read, perhaps because it was written on a phone. $\endgroup$ Jun 30 '20 at 20:25
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    $\begingroup$ Eek, my brain hurts $\endgroup$
    – MPW
    Jun 30 '20 at 20:33

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