I have 30 cups of juice 8% is apple. How many cups do i need to add to make it 10% apple

Answer 1

The problem is not well written as we can derivate two possible answers:

1.- The quantity of liquid is fixed. That is, if I add apple juice, I decrease the liquid of the othe kind, mantaining the total in 30

2 - The quantity of liquid is not fixed. That is, if I add apple juice, I mantaint the liquid of the othe kind, so the total liquid will be above 30.

Answering for case # 1:

You have 30 * 0.08 = 2.4 cups of apple juice in your 30 cups of juice. To make it 10% apple, you need to add 30 * 0.1 - 2.4 = 0.6 cups of apple juice. So the answer is 0.6

Answering for case # 2:

You start with 30 cups of juice, of which 8% is apple juice. That means you have 2.4 cups of apple juice (30 cups multiplied by 0.08).

Let's say you want to add X cups of 100% apple juice to this mixture. After you add X cups of apple juice, you will have (2.4 + X) cups of apple juice in total.

Your total juice mixture will now be (30 + X) cups. You want 10% of this new mixture to be apple juice, which can be written as:

(2.4 + X) = 0.10 * (30 + X).

Now, let’s solve for X:

2.4 + X = 3 + 0.10X.

0.90X = 0.6.

X = 0.6 / 0.90.

X = 2/3.

So, you need to add 2/3 cups (or approximately 0.67 cups) of 100% apple juice to the 30 cups of 8% apple juice to have a mixture that is 10% apple juice. Your final mixture will be 30 2/3 cups in volume.

Answer 2

.08(30) + x = .1(30+x)

2.4 + x = 3+.1x

.9x =.6

x=6/9=2/3 cup to get 10%

100-10=90

10-8=2

90/2=45= 30/(2/3)

you need 45 times as much 8% as 100% to mix to get 10%

45 times 2/3 cup = 30 cups