Ratio Problem

[dexter7889]

Okay, So This is probably easy compared to most of the problems presented on this website, but it would help immensely if I could recieve some help with it.

 

-The problem is as follows:

When mixing a quantity of paints, dyes of four different colours are used in the ratio of 7:3:19:5. If the mass of the first dye used is 3.5g, determine the total mass of the dyes used.

-I have Tried to construct an equation for this, but to no avail. This problem I believe is in relation to an earlier, simpler problem:

Problem 15. An alloy is made up of metalsA and B in the ratio 2.5:1 by mass. How much ofA has to be added to 6 kg of B to make the alloy?

Ratio A:B: :2.5:1 i.e. AB =2.5/1 =2.5

When B=6 kg, A/6 =2.5 from which, A=6×2.5=15kg

Any help at all would be highly appreciated.

Edited July 29, 2010 by dexter7889

[Sisyphus]

Well, you have the mass of the first dye, and you're looking for the mass of all the dyes put together. What ratio are those two quantities in?

[Mr Skeptic]

Yes, you got the second one right. The first one there is more than one way to do. You could do it like you did the second one, thereby also finding the masses of each pigment, or you could find the mass of all of them at once. But you'll have to show some work before we can help any more.

[dexter7889]

I took the advice and did this problem in the same format as the other question. I did get the answer right (answer key is in the back of the book), but I want to know if I arrived at the answer correctly.

This is how I did it:

-First I added up the 3 parts of the ratio that weren't given in grams (3+19+5=27). Then I put the two remaining numbers into a fraction (27/7) and divided. That gave me an answer of (3.857) Then I multiplied this by The original information given in the question (3.5g) by (3.857) which gave an answer of (13.545). Lastly I added that amount to the original info (13.545+3.5g). This in turn gave me a final answer of (=17.045g) or simply (17g).

 

-So, am I way out in left field, or was the method used appropriate? (BTW thanks very much for the replies to this post, and for the advice!)

 

 

[Mr Skeptic]

Yes, that is one of the correct ways of doing it. Another way would be to do the same ratio thing for each pigment. Another would be to have found what percentage the first pigment was of the total pigments and divided by that: 3.5 g * (7+3+19+5) / 7, which would have been the most similar to the way you did it. Incidentally, the correct answer would be 17 g even without rounding. You just got a slight difference due to rounding of the fraction you did first.

[dexter7889]

Yes, that is one of the correct ways of doing it. Another way would be to do the same ratio thing for each pigment. Another would be to have found what percentage the first pigment was of the total pigments and divided by that: 3.5 g * (7+3+19+5) / 7, which would have been the most similar to the way you did it. Incidentally, the correct answer would be 17 g even without rounding. You just got a slight difference due to rounding of the fraction you did first.

 

Alright, awesome. Thanks once again for the help, and for descriptions of multiple ways to solve this. I appreciate it! Cheers.