Question

Pls help me I got it wrongg :((

Answer 1

You are on the right track but it’s G) 4

Answer 2

4 ounces

Explanation:

I'm assuming when it says:
`33(1)/(3)%`% it means 33.3333333333 instead of 33/3.

Anyways under that assumption, we currently have 20 ounces in the grape juice, since 4 ounces is grape juice concentrate and 16 ounces is water. So currently let's just say that the total amount of grape juice concentrate is going to be:
`(4+x)` where x is the amount of grape juice concentrate you need to add to make it 33.33%. The next thing to know is how to calculate how much percent a is of b. This can be calculated using the equation:
`(a)/(b)*100`. So in this case the a is going to be the grape juice concentrate, and the b is going to be the entire mixture (water and grape juice). Since the concentrate is having x added to it, that means the entire thing is also having x added to it. This means we have the equation:
`(4+x)/(20+x) * 100`, since we already have 4 ounces of grape juice concentrate, and we already have 20 ounces in total (16 ounces of water + 4 ounces of grape juice). This is going to be equal to 33.33%, or in other words 33 1/3. So to make this a bit easier, I'm going to convert this mixed fraction into one fraction, this gives you the fraction:
`(100)/(3)`. So now that's all left to do is set these two expressions equal to each other and solve for x

Original equation

`(4+x)/(20+x)*100=(100)/(3)`

Divide both sides by 100

`(4+x)/(20+x)=(100)/(3)/ 100`

Keep fraction, change division to multiplication, flip 100

`(4+x)/(20+x)=(100)/(3)* (1)/(100)`

The 100 in the numerator will cancel out the one in the denominator

`(4+x)/(20+x)=(1)/(3)`

Multiply both sides by 20+x

`4+x=(20+x)/(3)`

Multiply both sides by 3

`3(4+x)=20+x`

Distribute the 3

`12+3x=20+x`

Subtract x from both sides

`12+2x=20`

Subtract 12 from both sides

`2x=8`

Divide both sides by 2

`x=4`

So Kahn needs to pour 4 more ounces of grape juice, to double check this, since the mixture already has 4 ounces of grape juice, this means the final mixture will have a total of 8 ounces of grape juice concentrate, and a total of 24 ounces, since it already had 16 ounces of water, and 4 ounces of grape juice and now there is 4 more ounces of grape juice being added, so a total of 24 ounces. this means that 8/24 will be grape juice concentrate or in other words:
`(1)/(3)` and when you multiply this by 100 (to convert to percent), you get 100/3 or 33 1/3%