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 non-juice.
92/100xx30=27.6 cups of non-juice. -
But now we want to increase the volume, by adding juice cups, until we have
10% juice. Let's make the amount addedx .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=27.6/0.90-30
x\approx0.66666... orx=0.\bar(6) - This is also known as
2/3 .
Therefore, you add two-thirds of a cup to the punch, and you will have10% 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