Comparing PricesDate: 09/29/2003 at 19:10:16 From: jeff Subject: word problems How do you calculate whether something is a better buy? For example, a 6-ounce can of tuna that sells for $1.59, or a package of three 3-ounce cans for $2.19? I'm not sure what the best way is to tackle the question. Date: 09/30/2003 at 13:30:17 From: Doctor Ian Subject: Re: word problems Hi Jeff, Whether something is a better buy depends on how it fits your needs. If you could get a can of tuna for $1.59, or a ton of tuna, all in one big can, for $100, the ton would definitely be less expensive per pound... but what could you do with it? It would start spoiling as soon as you opened it, so most of your $100 would be wasted. Having said that, note that when we divide two numbers with different units, we get a ratio, e.g., 26 miles in 1/2 hour = 52 miles/hour 38 grams in 19 cubic inches = 2 grams/cubic inch Similarly, we can get a ratio like $1.59 in 6 ounces = (1.59/6) dollars/ounce If we compute that for two different combinations, we can compare the results to find out which is cheaper. Note that we can compute either dollars per ounce, or ounces per dollar. In the former case, we want the smaller ratio. In the latter case, we want the larger ratio. However, having said that, the _easiest_ way to compare two prices like this is to convert them to a common quantity. That is, if I buy three 3-ounce cans for $2.19, that's 9 ounces for $2.19. If I double it, I get 18 ounces for $4.38. If I buy one 6-ounce can for $1.59, I can triple that to get 18 ounces for 3 times $1.59. Then the comparison is easy. Which way do I pay less for 18 ounces? Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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