Verified answer

currently, there are 2 cups of juice in the 40-cup mixture (2 is 5% of 40)

let x = juice to add to mixture

let 40 + x = volume of new mixture

(volume of juice in new mixture) / (total volume of new mixture) = .10 (10%)

(2 + x) / (40 + x) = .10

2 + x = .10(40 + x)

2 + x = 4 + .10x

.90x = 2

x = 2.222 cups

check:

2 + 2.222 = 4.222 cups juice

40 + 2.222 = 42.222 cups punch

4.222 / 42.222 = .10

You need to add 2 1/9 cups of grapefruit juice to get the desired concentration.

To do this, let x=the amount of grapefruit juice to be added

I always use this formula:

10%(x+40)=5%(40)+x

This formula says:

The left side is what you WANT TO GET. The right side is HOW YOU ARE GOING TO GET IT.

The left side:

x is how much you are adding, and 40 is what you have, so in total you have x+40 cups. Then they want 10% grapefruit juice, so multiplied by 10%.

The right side:

The first part is what you have. 40 cups of punch with 5% grapefruit juice. The second part is what you are adding, or x.

10%(x+40)=5%(40)+x

Now solve.

.1(x+40)=.05(40)+x

.1x+4=2+x

2=.9x

x=2/.9

x=20/9

If you divide, you get

x=2.2222222...

Which is 2 1/9 cups of grapefruit juice :)

Let x = no. of grapefruit cups to be added

2 = no. of grapefruit cups in present solution of 40 cups

Equation:

2 + x = 10% * (40 + x)

2 + x = 4 + 0.1x

x - 0.1x = 4 - 2

0.9x = 2

x = 2 / 0.9

x = 20/9 or 2 2/9 cups

Proof:

2 + (2 2/9) = 10% * (40 + 2 2/9)

4 2/9 = 4 + 2/9

4 2/9 = 4 2/9

Answer therefore is 2 and 2/9 cups

Okay, now you need to know the formula first.

%v/v = volume of soluble : solution volume x 100%

%v/v means volume in percentage.

The old %v/v is 5% (or 0,05).

The grapefruit volume (volume of soluble) is 5% out of the total solution volume, which is 40 cups. That means 2 cups.

The solution volume is 40 cups.

Okay, now you want to get 10% grapefruit. Now, think logically. If we want to have MORE grapefruit concentrate inside the punch, do we have to add more grapefruit juice (soluble) or water/ice (solvent)?

As you may have thought (in your question), the answer is that we have to add MORE grapefruit juice (soluble) while keeping the water/ice (solvent) remains unchanged. However, the solution volume will change because of we add more soluble.

So, the new formula (to get 10% grapefruit juice) would be:

NEW %v/v = (volume of current soluble + volume of NEW soluble) : (current solution volume + volume of NEW soluble) x 100%.

So:

0.1 = (2 + a) : 40 [we don't need to put x 100% because I have simplify 10% into 0.1]

0.1 = 2 + a

-------------------------

1 = 40 + a

[cross multiplication]

2 + a = 0,1 (40 + a)

2 + a = 4 + 0.1a

0.9a = 4 - 2

0.9a = 2

a = 2 : 0,9

a = 2.2222

volume of new soluble needed = a

volume of new soluble needed = 2,2222 cups

So, to make a punch containing 10% grapefruit juice, we need to add 2 CUPS OF GRAPEFRUIT JUICE.

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Currently there are 2 people who rated my answer as a bad one, but I guarantee that this answer is correct.

If you don't believe me, you can try by yourself at home (seriously!) and you'll find that you only need to add a 2.2 cups of grapefruit juice.

I hope this answer helps you.

you just have to add 2.22222222222 cups.

right now you have 40 cups and a concentration of 5%

that translates into the equivalent of 2 cups of grapefruit and 38 cups of punch.

if you add 2.2222222 cups of grapefruit you end up with 4.222222222 cups of grapefruit in 42.222222222222 cups total.. that's 10%

8 more cups,

wrong

hang on if you got 40 cups of juice, with 5% grapefruit it already contains 2 cups of grapefruit.

So if you add another 2.2 cups of grapefruit it will contain 42.2 cups of juice with 4.2 cups of grapefruit, or 10.048% grapefruit

80 cups of grapefuit juice i think

im only 13 anyways