A carpenter has a bag, containing 2 types of nails, which weighs 3 pounds. Finishing nails weigh 150 nails/pound. Framing nails weigh 30 nails/pound. The ratio of finishing nails to framing nails is 25:1. How many finishing nails in the bag?  

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We are given that a given bag containing two types of nails weighs 3 pounds. There are finishing nails that weigh 1 pound for every 150 nails, and framing nails that weigh 1 pound for every 30 nails. We are also told that the ratio of finishing nails to framing nails is 25:1. We are asked to find the number of finishing nails in the bag:

Let x be the number of finishing nails, and let y be the number of framing nails.

The total weight of finishing nails is given by x/150 while the weight of framing nails is y/30.(e.g. if there are 300 finishing nails they weigh 2lbs, etc.)

Since the weight of the bag is 3 lbs, we have x/150 + y/30 = 3.

We also know that x=25y (since they are in a ratio of 25:1). We can substitute 25y in place of x to get:

`(25y)/(150)+y/30=3 ` or `y/6+y/30=3 ==> (5y)/30+y/30=3 ==> (6y)/30=3 ==> 6y=90 ==> y=15 `

If y=15 then x=25y=25(15)=375

There are 375 finishing nails in the bag.

There are many other ways to approach this problem including using a guess-and-check system, graphing, etc.

Checking the answer we see that 375 finishing nails weigh 2.5 pounds while 15 framing nails weigh .5 pounds with a total weight of 3 pounds as required.

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