How many cup of juice must be added to 30 cup of punch that is 8% grapefruit juice, to obtain a punch that is 10% grapefruit?
2 Answers
Explanation:
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You have
#30# cups.#8%# of those cups are grapefruit juice. To
calculate:#8/100xx30=2.4# cups are juice.Remember that 92% of this punch is nonjuice.
#92/100xx30=27.6# cups of nonjuice. 
But now we want to increase the volume, by adding juice cups, until we have
#10%# juice. Let's make the amount added#x# .Thus,
#30+x# cups will be our new total punch volume.  We will still have 27.6 cups of punch that is NOT juice! But in our new volume, that will only be
#90%# of the punch.
#27.6/((30+x))=90/100#
#90/100(30+x)=27.6#
#0.90(30+x)=27.6#  Let us solve for
#x# to find the amount of grapefruit juice added.
#27.6/0.90=30+x#
#x=27.6/0.9030#
#x\approx0.66666...# or#x=0.\bar(6)#  This is also known as
#2/3# .
Therefore, you add twothirds of a cup to the punch, and you will have#10%# juice.
Checking results:
Remember that we had
 Let's divide to calculate how much of our new amount is juice.
#(2.4+2/3)/(30+2/3)=0.1#  To get percentage, multiply by 100%.
#0.1xx100%=10%\color(green)(√)#
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This means
You want
That means
To get from 2.4 cups to 3 (8% to 10%), we need to subtract:
We need 0.6 cups of juice to get 10% grapefruit juice punch.
Another method:
So we need a
Let's multiply:
Much better to stick to fractions as rounding errors occur when using decimal.
Explanation:
Lets consider the information we have been given:
Let the volume of the 8% juice be
Let the volume of the 100% juice be
Let the blend volume of 10% juice be
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Using the above information consider volume:
Using the above information consider percentage:
but from
Also we know that
Multiply both sides by 100
Note that