Ratio Word Problems: Fill & Download for Free

Okay, okay. We know you’re trying to get your homework answered on here. We’ll be cool about it. Just copy this answer verbatim, and I swear your teacher will be thrilled with it.First, we need to translate the mass of the cake into volume, because nobody apart from the rest of the world outside the U.S. or professional pastry chefs bake by mass instead of volume. Claudia is going to be using cups and pints and teaspoons, in all reality.You know what 5kg works out to in pounds? Eleven. Eleven pounds of cake. A typical large sheet cake is maybe five to six pounds.What is Claudia baking here? A wedding cake? This is enough cake to feed the entire class sufficient to give everyone a sugar high that will totally wreck the afternoon.Eleven pounds of cake, and 75% of it is flour?This cake is gonna suuuuuuuuuuck. Perfect cake? Ugh. No. This word problem writer needs to be banned from any pastry kitchen in the world.Allow me to let you in on a little secret to baking good cakes that will scale up about as much as you ever need. It’s the 1:1:1:1 rule.Cakes are really comprised of four ingredients: flour, butter, sugar, and eggs. Note that there’s no cream in there. A flour cake with cream would be… weird, to say the least. Baking that would just result in a dense rock of a cake. You know what you’ve made there? Dry, milky glue. Not a cake. 3:1 flour to cream wouldn’t even make a batter. This is a terrible, terrible cake.But anyways, 1:1:1:1, flour, butter, sugar, eggs. That will make the perfect pound cake. Fun fact, that’s why it’s called a pound cake, because you’d use one pound of each of these. True story.Right. Back to the word problem. A cup of flour is about 4 1/4 ounces. The cake is going to be just over eleven pounds. That translates to… 176.3696 ounces, which we’ll round up to 176.4. 75% of that is flour, so that’s 132.3 ounces of flour. With a little mathematical magic, that means we’re looking at 31.1294117647 cups of flour. We’ll round that off to 31 1/8 cups of flour, give or take a little.Man, that’s a lot of flour. This is going to take a couple of bags of flour.Although, that’s using King Arthur Flour. Gold Medal Flour says that it’s more like 3–1/3 cups per pound. Crap. All right, let’s switch to Gold Medal Flour here and try again. 132.3 ounces of flour for our eleven pound cake means… 40.0909090909 cups of flour. I think we can safely just round that down to 40 cups even. Still going to be a couple of bags of flour here.A cup of heavy cream in the U.S. is just over half a pound. With an eleven pound cake that’s supposed to be 25% cream, that’s going to work out to about 2.75 pounds of cream. We can work backwards here to figure out that rounds off to 5 3/4 cups of cream. 16 cups in a gallon, four in a quart, so Claudia needed to buy 2 quarts of cream here. Now, if she bought enough cream for 11 pounds and 35% of it to be cream, she’d have needed 3.85 pounds of cream, or just shy of eight cups of cream, which would be two quarts. So, she’s golden on cream and doesn’t need to buy any more, which the word problem already told you, I suppose.So, flour. We said we needed 40 cups of flour in our “cake,” which is still going to be a really terrible cake, but whatever. I said I’d help you with this homework, and so I shall.Gold Medal Flour says there’s approximately 17 cups of flour in each 5-pound bag of flour. We needed 40 cups of flour here.Wait, wait… we’re missing some information here. Did Claudia buy 5-pound bags of flour, or 2 pound bags of flour? Or is she buying in bulk from some place like Costco, and bought a 10 or 20 pound bag of flour?If she’s already bought a 20 pound bag of flour, she’s clearly got enough flour already to just fix the ratios and bake a eleven pound flour-and-cream “cake.” Even a 10lb bag is going to be sufficient.But, the problem does imply that maybe she just mixed up the ratios and thought it was 65% flour. 65% of eleven pounds works out to 7.15 pounds of flour.So, let’s assume that she bought a 5lb bag of flour and a 2 lb bag of flour. Which was going to be insufficient anyway, and if she’d done any math before going to the store, she’d have figured that out. But, I’m assuming she figured she could skimp a little on the flour, since she could get away with buying just under what she needed. After all, she’s just short by about half a cup or so. She can borrow that from her neighbor.Claudia is probably a woman on a budget. She clearly doesn’t cook or bake very often and would have no use for excess flour laying about her apartment. So, she wants to buy the bare minimum flour needed to complete this word problem.So, we’ll assume that she bought the 5lb and 2lb bag of flour, thinking she’d have enough, and it turns out she doesn’t, because what she really needs is 8 1/4 pounds of flour for this eleven pound cake.Since she’s got 7 pounds of flour already, and honestly, she really just needed a bit more anyway, what she needs is another 2lb bag of flour from the store.2 pounds converts to .9 kilograms.So, that’s how many more kilograms she’ll need to buy at the store: nine-tenths of a kilogram, (which is really a 2 pound bag, and your teacher should know that they sell it that way).There you go. You just copy that right down and submit that word for word. I won’t tell on you. Pinkie swear.

You'll be tested on Math, English, Logical reasoning, data interpretation, accounts and tax.For math, just go through those word problems we did in the 10th and a few sums on ratios (not financial ratios). English is easy - no need to prepare. For tax, study the due dates for ST, TDS, TP, etc. Accounts again, is manageable.Good luck!

It's like asking, "now that we have spell-checkers, why bother with English class?" Spelling is a small and trivial portion of English class. Just so the manipulation of equations in algebra.Unfortunately, drill work has swollen up until it consumes nearly the entire algebra curriculum. It's as if students in English class learned the definitions, spelling, and parts of speech of 20,000 vocabulary words, but never learned of Shakespeare, Hemingway, or Orwell, much less wrote their own work.In algebra class, students who use computers to do the grunt work could focus more on applying algebra to real situations, and thereby understanding what it does. When I supported myself as a private tutor, parents repeated told me, "my son is really good at math. He's just having a little trouble with word problems." Most people honestly think that if you can solve a quadratic equation, you understand algebra, but there's just this little extra thing called "word problems" that is one last detail you have to take care of.For example, in algebra class students could start developing the intuition that I use as a physics student every day. It is important to understand intuitively the differences between logarithmic growth, linear growth, super-linear but sub-exponential growth (e.g. x^2), exponential growth, and superexponential growth. These concepts come back in calculus, but understanding and applying them first in algebra class is a good start.I also use algebra to answer questions by referring to the way things scale - volumes proportional to length cubed, areas proportional to length squared, and therefore surface area-to-volume ratio inversely to length. That has important consequences in things like biology (why do large cells have so much internal structure while bacteria are just bags of jelly?) and thermodynamics (why is flour explosive, but not bread?). That's the sort of intuition and application you could learn in algebra class, but you don't because you're too busy doing the work that computers ought to do for you.Students who don't have to do endless drill work could also do problem solving of the sort currently reserved for math competitions. They could learn new and related concepts such as group theory. Math is incredibly rich, as you can learn by picking up a serious survey book like the Princeton Companion or a recreational book like those of Martin Gardner.It's a sin that such a tiny portion of math is taught in math class, and that the portion we focus on is dull and rote. The way we do math class now is symptomatic of teachers being overworked, underpaid, and undereducated, of the homogenization impressed by state-mandated standards and tests, and of the now-ingrained cultural attitude towards math.If we were truly freed from the "do problems 17 to 53 odd" paradigm of math class, students would spend more time engaging in ideas, learn more, find that class more enjoyable, and begin to view it as a genuine lifelong intellectual outlet the way literature is.Since you asked about WolframAlpha in particuliar, you may be interested in what Conrad Wolfram (Steven's brother) has to say on it.Further reading and viewing:Lockhart's Lament is the most famous essayhttp://www.maa.org/devlin/LockhartsLament.pdfVi Hart's videos:http://www.youtube.com/user/Vihart?feature=watchThe entire world of recreational mathematics:http://en.wikipedia.org/wiki/Recreational_mathematicsThe Art of Problem Solving, which provides great books and some softwarehttp://www.artofproblemsolving.com/