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Ratios, rates, and proportions — Harder example

Watch Sal work through a harder Ratios, rates, and proportions problem.

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  • blobby green style avatar for user Maimoona
    I am seriously losing hope as I watch more complex videos and do more complex math problems
    (63 votes)
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    • duskpin ultimate style avatar for user Cowboy
      So, real quick... without writing and quickly using your head (not a calculator) you can figure out this one!
      To make this easier to see, simply take his ratio in the problem (1cm = 20ft) and square it out. Yes, he did this, but wrote a lot. All you need to write down during the test is basically the 20 (if you need to see it to remember it is there). It is 400 because 2 squared is 4 (then put the zeros back in place to make it 400)
      Next, we already see that 400 square feet is what 1 pound will cover. Under the entire field, there are 180 sections of 400 square feet. that's 180lbs. Done and only 5 seconds out of your 55 minutes (or whatever section this is in)! 😊
      If you have a mind for patterns, ratios, rates and proportions are easy. But if not, that's ok because often times you will have the tendency to be able to handle many more types of problems I will never be able to ever figure out! 😉
      (70 votes)
  • male robot johnny style avatar for user saba fatima
    this question is troubling me:
    There are 78 biscuits in a box. Some are salty and the rest are sweet. Which of the following could be the ratio of salty to sweet biscuits in the box?
    A) 3:4 B) 4:1 C) D) 5:8 E) 1:3
    (9 votes)
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    • blobby green style avatar for user Junsub (Kevin) Lee
      E has to be the answer. Unless the biscuits are broken and you are considering bits of pieces of biscuits, the only number in the given options that divides 78 perfectly is the number 3. For example 78/3=26. However, 78/4=19.5 and since there aren't half biscuits when considering ratios of salty and sweet biscuits, all answers with 4 is wrong eliminating A, and B. C is not the answer because both 5 and 11 does not result in an integer. 78/5=15.6 and 78/11=7.09 eliminating C, thus since D has 5 as well, it cannot be the answer. Also the 8 in D results in a 9.75 which does not make sense. Therefore, the only reasonable answer is E containing 1 and 3, both resulting in a integer when dividing 78.
      (15 votes)
  • old spice man blue style avatar for user shivanksharma2332
    For this question, instead of doing all that work to get 180 pounds, wouldn't have it been much simpler to realize that for every square centimeter, it is 400 square feet, and for every 400 square feet, it's one pound of seed, so then you would need 180 pounds of seed?
    (21 votes)
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  • blobby green style avatar for user Abigail Fordyce
    Will they give you the conversions on the SAT or will we have to memorize the actual conversations?
    (7 votes)
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  • blobby green style avatar for user Oluwateniola Ayeni
    Guys i'm new here
    right now i just need some encouraging words
    i'm beginning to loose hope on sat
    (8 votes)
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  • male robot donald style avatar for user My Nguyen
    Hi guys. Do u know which sections in the SAT allow to use calculator ?
    (5 votes)
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  • blobby green style avatar for user arodriguez24
    Dam I guess everyone thought it was 9
    (6 votes)
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  • duskpin seed style avatar for user Dodi Hazem
    not going to lie but when I read the question before he solved anything I thought the answer was 9 because I divided 180 by 20 and after he solved it it made much more sense because, with my answer, the field would be small compared to the right answer.
    (6 votes)
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  • blobby green style avatar for user anungoo0531
    i thought the answer would be 9 since x= number of pounds of seed she need to cover the entire field 3600/x=400/1 400x=3600 x=9pounds
    (4 votes)
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  • aqualine seed style avatar for user kmorris
    what's the difference between unit price and unit rate?
    (2 votes)
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    • duskpin sapling style avatar for user Lin Gh.
      Well, a rate is the ratio between two related quantities. Like, meter per second (m/s), dollar per gram, gram per milliliters (g/ml), etc.

      Units are used for measurement, like how much is going to make "1" unit of something. Units in price could be dollars, cents, euro, pound, yen, franc, etc.

      Hope this is what you're looking for.
      (3 votes)

Video transcript

- [Instructor] Erika plans to purchase seed to plant grass in a large field. She has a map of the region, and calculates the area of the region on paper to be 180 square centimeters. The scale on the map shows that one centimeter is equal to 20 feet. So they're giving us linear centimeters to linear feet, not square centimeters to square feet, so I think we're gonna have to figure that out. If Erika plans to cover every 400 square feet with one pound of seed, approximately how many pounds of seed will she need to cover the entire field? So what we wanna do is we wanna figure out, well, how many square feet is the field? How many square feet is the field? And we know on her map, her map has, well, a map of the field, and she's, on the map it's 180 square centimeters. And they tell them or they tell us that one centimeter is equal to 20 feet. But if this is square centimeters, then we wanna convert this to square feet. So to convert, if one centimeter's equal to 20 feet, to convert it from, if we wanna figure out the conversion from square centimeters to square feet, we could just square both sides of this. We could just square both sides of this. And what will that be? One squared is still one, but now we have one centimeter squared. And I could write it like this just to be clear that I took both of them to the second power, but one squared is just one. And this is going to be equal, 20 squared is going to be 400 square feet. So one square centimeter on this map is going to be equal to 400 square feet. So how many square feet does 180 square centimeters represent? So I could write 180 centimeters squared. And we know that every centimeter squared represents 400 feet, or we could say 400 feet squared per centimeter squared. And we want the units to cancel out, so this makes sense. You have centimeters squared over centimeters squared. So the actual field is going to be 180. 180 times 400. Times 400 square feet. And that makes sense. The region on paper was 180 square centimeters. Each square centimeter is equal to 400 square feet in reality. So for each of those square centimeters, it's going to be 400 square feet. So it's 180 times 400. So this is the area in square footage of the actual field, and then they tell us we're gonna use one pound of seed. One pound of seed for every 400 square feet. So let's see, the area of the entire field, let me give myself a little bit more space, is, and I'm not gonna even multiply it out because this 400 is showing up, so this seems useful. So the area is 400 feet squared. I just wrote that. And we're going to use one pound, one pound of seed, pound of seed, for every 400 square feet. For every 400 square feet. And if we look at it, the units cancel out. Square feet divided by square feet. Then we have 400 divided by 400. And we're left with 180 times one pound of seed, which tells us that we're going to use 180 pounds, 180 pounds of, 180 pounds of seed, which is that choice right over there. Now, if you're under time pressure on the SAT, although I would be careful, because this one is a little bit, it could be a little confusing. But you might've said, okay, there's 180 square centimeters. Each of those square centimeters is 400 feet. This is actually the key thing that you have to realize, that each square centimeter is not just 20 feet. It's 400. It's 400 feet. So you're gonna have 180 times 400 square feet for the entire field. But then each of those 400 feet, each of those 180 400 square feet, you're gonna use one pound of seed. You're gonna use 180 pounds of seed. So you could've done it without all of this writing, but it is helpful to write it so that you don't confuse things.