# Lesson: Introduction to Ratios

## Comment on Introduction to Ratios

### Shouldn't the last step

Shouldn't the last step rather be: Multiply the equal parts into the target ratio instead of divide? ### Perhaps the better word is

Perhaps the better word is "distribute"
Say we have 12 cookies to be divided into a 1:2 ratio.
1 + 2 = 3 (e.g., T = 3)
So, 12/3 = 4 (i.e., 4 cookies per batch)
Now distribute the 4-cookie batches into a 1:2 ratio.
We get: 1 batch : 2 batches

### Thank you!:)

Thank you!:)

Your videos are too helpful. But I have one comment to make the last two questions easier. Just divide the total number of cookies (15) by the ratio sum (3), then multiply the result (5) by each portion of the ration (1*5) and (2*5). So, you will not need the distribution. Also, can be done on the tree ratios. ### Thanks for that suggestion,

Thanks for that suggestion, Moamen.

We are pretty much using that same technique in the video, except we take a take a couple of extra steps to show why/how that technique works.

### OK, thanks for this great

OK, thanks for this great effort that is shown in new techniques you use and the way you are presenting Math.

### In the oil/vinegar/water

In the oil/vinegar/water ratio problem, I am not understanding how we know we can use all 8 cups of oil with the given information. Can you provide more details please. Thanks ### Question link: http://www

Good question, Jay.

Since the oil/vinegar ratio is 3/2, I know that I'm going to use a lot more oil than vinegar. In fact. for every 2 drops of vinegar added to the mixture, we must add 3 drops of oil. So, the amount of oil needed is 50% more than the amount of vinegar needed.

We have 8 cups of oil and 7 cups of vinegar. Since the volume of available oil is NOT 50% more than the volume of available vinegar, we can see that we're going to run out of oil before we run out of vinegar. In other words, we'll end up using ALL of the oil and only SOME of the vinegar.

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

Alternatively, let's see what happens if we try to use ALL of the vinegar.

The oil/vinegar ratio is 3/2. Let's let x = the volume of oil needed to mix with the 7 cups of vinegar.

Using equivalent ratios, we get: x/7 = 3/2
When we solve this equation for x, we get x = 10.5

So, if we want to use all of 7 cups of vinegar, we'll need 10.5 cups of oil (to maintain the 3/2 ratio). However, we don't have 10.5 cups of oil. So, this approach won't work.

Does that help?

Cheers,
Brent

### Yes sir. Thank you so much.

Yes sir. Thank you so much.

Jason

### In a similar question like

In a similar question like this on The GRE prep plus book,they added the ratio of reptile to bird (7+2) and then the final ratio of reptile to the total was 7/9. I'm confused now cuz yours was simply 7/2 ### Hi Stunnerxoxo,

Hi Stunnerxoxo,

It's hard to comment on your post if I don't know which question from the GRE Prep Plus book you're referring to.
If you can find the question and post it here, I'd be happy to help.

Cheers,
Brent

### https://greprepclub.com/forum

https://greprepclub.com/forum/the-ratio-of-the-number-of-manufacturing-industry-workers-wh-1882.html

Manufacturing = 2 million
Service = 1.28

I multiplied both sides by 100 to get 200:128.
Simplifying further, I get 25:16 and then I take a square root of both sides to get 5:4 which leads to incorrect answer.
I can't take square root for ratios? ### Question link: https:/

When it comes to creating equivalent ratios, we have only 2 options:
1) MULTIPLY both parts of the ratio by the same value
2) DIVIDE both parts of the ratio by the same value

For example, start with the ratio 1 : 2
MULTIPLY both parts of the ratio by 12 to get 12 : 24, which is EQUIVALENT to 1 : 2

Now take 12 : 24 and DIVIDE both parts of the ratio by 4 to get 3 : 6, which is EQUIVALENT to 12 : 24 and 1 : 2

Now let's see what happens when we try operations other than multiplication and division:

For example, take the ratio 1 : 2 and ADD 12 to both sides to get 12 : 13
Hmmm, the ratio 12 : 13 is NOT EQUIVALENT to 1 : 2

Another example: take the ratio 7 : 14 and SUBTRACT 5 from both sides to get 2 : 9
The ratio 2 : 9 is NOT EQUIVALENT to 7 : 14

Another example: take the ratio 25 : 100 and take the SQUARE ROOT SUBTRACT of both sides to get 5 : 10
The ratio 25 : 100 is NOT EQUIVALENT to 5 : 10

So, the only ways create EQUIVALENT ratios are:
1) MULTIPLY both parts of the ratio by the same value
2) DIVIDE both parts of the ratio by the same value

Cheers,
Brent

### hi! I found this question

hi! I found this question very confusing: https://greprepclub.com/forum/oil-vinegar-and-water-are-mixed-in-a-3-to-2-to-1-ratio-to-10427.html

Since it take 3:2:1 proportion to make salad dressing, shouldn't the answer be two cups of salad dressing, since there's only enough oil to make two batch (3*3 would be 9 and would exceed the oil available)

Also, Why did you multiply each part of the ratio by 8/3 instead of 8? ### My solution: https:/

The question. The key here is that the the volumes of oil, vinegar, and water need not be INTEGERS.
We know this because the question tells us that "fractional cup measurements are possible."

Q: Why did you multiply each part of the ratio by 8/3 instead of 8?
A: It's given that oil:vinegar:water = 3:2:1
We're also told that we have 8 cups of oil
So, we want to create a ratio that's equivalent to 3:2:1 such that the first value (cups of oil) is 8.
To do this, we need to take 3 and multiply it by 8/3 to get 8

Does that help?

### Hello sir, this question is

Hello sir, this question is also done using unitary method or proportion method by someone else called venom004.
Is their method correct?

"I solved it like this:

From 3 cups of oil, you get (3+2+1) = 6 cups of salad
then from 8 cups of oil, you get (6/3)*8 = 16 cups of salad"

Is the above proportion method useful too? ### Yes, the proportion method is

Yes, the proportion method is a useful strategy (which I cover at 4:55 in the above video).

The key factor in using that strategy to solve the question is to first recognize that the volume of OIL is the limiting factor. If we had applied the same technique to the volume of VINEGAR, we'd get a different answer.

### https://gmatclub.com/forum/a

https://gmatclub.com/forum/a-perfect-cake-should-have-25-cream-and-75-bread-oman-bought-materi-289765.html for this problem from looking at past videos I understand that in most cases a ratio is a part to part relationship. how come in this question I cant compare a part to whole relationship? Ex saying that we have (3.25 +x) / (5) = 75/100 and solve for x when i did this it did not work. I got the right answer when doing a part to part relationship. So my question is when can e use a part to part vs a part to whole relationship when considering ratios? ### Question link: https:/

The problem with your solution is that it assumes we are trying to make a perfect cake that weighs exactly kg.

Since the weight of the EXTRA bread will contribute to the overall weight of the cake, your equation should look as follows:
(3.25 + x)/(5 + x) = 75/100

Solve to get: x = 2 kg ### Question link: https:/

The problem with your solution is that it assumes we are trying to make a perfect cake that weighs exactly kg.

Since the weight of the EXTRA bread will contribute to the overall weight of the cake, your equation should look as follows:
(3.25 + x)/(5 + x) = 75/100

Solve to get: x = 2 kg

### https://gmatclub.com/forum

https://gmatclub.com/forum/the-interior-of-a-rectangular-carton-is-designed-by-a-certain-110002.html
I thought this was an interesting problem and wanted to see if my approach is correct. So i took y as the multiplier and said 3y*2y*2y = 12y^3 =x solve for y and i get y = (x/12)^(1/3)to find the height I multiply times 2 so the height becomes 2 * (x/12)^1/3 and then thats as far as i can get without the solutions. Is that thinking process correct? ### Question link: https:/

That approach is perfect, Ravin.

From there, we can recognize that 2 = 8^(1/3)

So, (2)(x/12)^1/3 = (8)^(1/3) * (x/12)^(1/3)
= (8x/12)^(1/3)
= (2x/3)^(1/3)
= B