100 Percent of Daily Allowance of IronDate: 09/30/2001 at 18:30:48 From: Amy Subject: Percentage Word Problem A common foodstuff is found to contain .00125% iron. The serving size is 87.0 grams. If the recommended daily allowance is 18mg of iron, how many servings would a person have to eat to get 100% of the daily allowance of iron? About all I know at this point is .018 grams = 100% iron. I thought maybe if you found out how many times .00125 goes into 100, for 100%, you could figure something out, but I'm not sure. Please help. Amy Date: 10/04/2001 at 10:49:43 From: Doctor Ian Subject: Re: Percentage Word Problem Hi Amy, If the foodstuff is 0.00125% iron, then there are 0.00125 grams of iron for every 100 grams of the foodstuff. This follows from the definition of 'percent', so make sure you see why it's true. (Write back if you don't see why it's true!) 0.00125 grams is the same as 1.25 milligrams: 0.00125 0.0125 0.125 1.25 ------- = ------ = ----- = ---- 1 10 100 1000 So there are 1.25 milligrams in 100 grams of foodstuff. If a person needs 18 milligrams of iron, how many times does he need to eat 1.25 milligrams of iron? Well, if he eats 1.25 milligrams 10 times, that's 12.5 milligrams, which means he has to eat 5.5 more milligrams. If he eats 1.25 milligrams 4 more times, that's 5 milligrams, which gets him up to 17.5 milligrams. So he has to eat 1.25 milligrams of iron about 14 times to get up to 18 milligrams of iron. Now, each time he does that, he has to eat 100 grams of the foodstuff. That adds up to about 1400 grams of foodstuff. Now the question is: How many 87-gram servings does he have to eat in order to eat 1400 grams? Again, if he eats 10 servings, that's 870 grams, which leaves him about 530 short. If he eats 3 more, that's 261 grams, which still leaves him 270 short. If you keep going, you'll end up with the approximate number of servings. It's important to note that I'm not just looking for the magic, one-shot equation that will solve the problem. Instead, I'm trying to think through each step, so that I understand what's going on, and I can have some confidence that I'm on the right track. At the end of all this, I might come up with an equation, or I might not. But if I do, I'll know exactly where it came from. There is also another way I could go about this, which would be to play with dimensions. For example, I start out knowing that a daily requirement is 18 milligrams: 18 mg = (mg per serving) * (number of servings) So if I can figure out how many mg are in a serving, I'm in good shape. How can I do that? Well, I have to start with what the problem gives me, which is mg per 100 grams: 1.25 mg iron ? g foodstuff 18 mg iron = --------------- * -------------- * (number of servings) 100 g foodstuff ? servings I don't know what numbers go in the middle yet, but I know what the dimensions have to be in order for the dimensions I don't want to cancel out properly. Now, in fact, having written it out this way, I can see that I _do_ know what numbers have to replace the question marks. The problem tells me that a serving is 87 grams of foodstuff. So I know that 1.25 mg iron 87 g foodstuff 18 mg iron = --------------- * -------------- * (number of servings) 100 g foodstuff 1 serving Now I can see that my dimensions will cancel out the way I need them to: xxxxxxxxxxx 1.25 mg iron 87 g foodstuff 18 mg iron = --------------- * -------------- * (number of servings) 100 g foodstuff 1 serving xxxxxxxxxxx (1.25 * 87) mg iron = ------------------- * (number of servings) (100 * 1) servings Now, just looking at the numbers, I can see that 87 is a little smaller than 100, and 1.25 is a little larger than 1, so this whole thing should come out to be about equal to 1: ~ = 1 * (number of servings) which means that I'd need about 18 servings. Does that seem reasonable? Well, working the other way, we got around 16 servings, so this is in the ball park. If you use a calculator to work out the exact answer, you'll get something slightly different, but not _too_ different. As I said, there are lots of different ways to go about solving any problem, and any solution that you _know_ must be correct is preferable to a solution that you _hope_ is correct. For example, here is a very simple, if not very elegant, way to solve the problem: A common foodstuff is found to contain .00125% iron. A serving size for the foodstuff is 87.0 grams. Each serving must then contain 0.00125 0.00125% * 87 g = ------- * 87 g (definition of percent) 100 = 0.0010875 grams of iron If the recommended daily allowance is 18mg of iron, 18 milligrams is 18 thousandths of a gram, or 18/1000 grams, or 0.018 grams. how many servings of this foodstuff would a person have to eat to get 100% of the daily allowance of iron? This is the same as asking: How many times do I need to eat 0.0010875 grams of iron at a time, in order to eat a total of 0.018 grams of iron? Which is another way of asking, how many times does 0.0010875 go into 0.018? So in this solution, I haven't done anything tricky at all. I just had to understand what a percentage is, and how to compute the number of times you have to eat some small amount of stuff in order to eat some total amount of it. Although teachers often insist that you solve a particular kind of problem using a particular set of steps, in the real world only two things matter: (1) that you come up with the right answer, and (2) that you _know_ it's the right answer, without having to ask anyone else to check that for you. If that means that you have to draw pictures, or even count on your fingers, then that's perfectly okay. I hope this helps. Write back if you'd like to talk about this some more, or if you have any other questions. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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