Question

Pls help me I got it wrongg :((

Answer 1

Answer:

4 ounces

Step-by-step explanation:

I'm assuming when it says: $33\frac{1}{3}%$% 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: $\frac{a}{b}*100$. 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: $\frac{4+x}{20+x} * 100$, 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: $\frac{100}{3}$. So now that's all left to do is set these two expressions equal to each other and solve for x

Original equation

$\frac{4+x}{20+x}*100=\frac{100}{3}$

Divide both sides by 100

$\frac{4+x}{20+x}=\frac{100}{3}\div 100$

Keep fraction, change division to multiplication, flip 100

$\frac{4+x}{20+x}=\frac{100}{3}* \frac{1}{100}$

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

$\frac{4+x}{20+x}=\frac{1}{3}$

Multiply both sides by 20+x

$4+x=\frac{20+x}{3}$

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: $\frac{1}{3}$ and when you multiply this by 100 (to convert to percent), you get 100/3 or 33 1/3%

Answer 2

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