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Ratios, rates, and proportions — Harder example

Video transcript

erricka 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 a hundred eighty square centimeters the scale on the map shows that one centimeter is equal to 20 feet so they're giving us linear centimeters two linear feet not square centimeters two square feet so I think we're gonna have to figure that out if Erica plans to cover every four hundred square feet with one pound of seed approximately how many pounds of seed will she need to cover the entire field so what we want to do is we want to 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 her map has couple a map of the field and she's on the map it's 180 square centimeters and they tell them or they tell her they tell us that one centimeter is equal to 20 feet but if this is square centimeters so we want to convert this to square feet so if you to convert if one centimeter is equal to 20 feet to convert it from if we want to 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 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 400 400 square feet so one square centimeter on this map is going to be equal to 400 square feet so how many how many square feet does 180 square centimeters represent so I could write look I could write 180 centimeters centimeter squared and we know we know that every centimeter squared represents 400 feet or we could say 400 feet squared per centimeter squared and we want the unit's 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 4 100 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 going to 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 them 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 we're going to use one pound one pound of seed pound of seed for every 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 and 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 pounds 180 pounds of 180 pounds of seed with it which is that choice right over there now if you're under time pressure on the ICG although I would be careful because this one is a little bit it could be a little bit confusing but you might say okay there's 180 square centimeters each of those square centimeters is 400 feet this is actually the key thing that you had to realize that not each 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 so it's going to use you can use 180 pounds of seed so you could have done it without all of this writing but it is helpful to write it so that you don't you don't confuse things