While touring through Europe, alfred finds that $1 is equal to 7 Drachmas, and that 5 drachmas is equal to 3 quilos. What is the ratio of dollars to quilos?

While touring through Europe, alfred finds that $1 is equal to 7 Drachmas, and that 5 drachmas is equal to 3 quilos. What is the ratio of dollars to quilos?

we want to set up an equation b/w dollars and quilos. easiest way is to insert how much Quilos is worth a Drachma=> use eq.2 and divide both sides by 5 then you get Drachma=3Q/5.
when you put in that value into Drachmas in eq.1, you will get 1 dollar = 21Q/5. since you want dollars/Q, just simply divide both sides by Q, and you will have the answer 21/5.
Hope that helps

1$ x 1/7 drachma x 5 drachma/3 quilos then you just multiply and divide and you are left with 5$/21quilos which is the ratio you want. It's pretty much the same way you can do stoichiometry problems if that helps.

Hey there,
The answer given by the Destroyer is correct. You are on the right track, except you have the units (in this case the currency) mixed up. Usually this is the method I use and hopefully It will help you clear this up.
So 5 Drachmas = 3 quilos
then 1 Drachma = 3/5 quilos correct?
Now the second part:
1 dollar = 7 Drachmas
and if 1 drachma = 3/ 5 quilos, multiply 3/5 and 7
There.. 1 Dollar = 21/5 quilos..

I hope it helps, this way of solving questions usually helps me out a lot in gen chem too (dimensional analysis technique is similar, cancel out terms you dont need while keeping the ones you do)

1$ x 1/7 drachma x 5 drachma/3 quilos then you just multiply and divide and you are left with 5$/21quilos which is the ratio you want. It's pretty much the same way you can do stoichiometry problems if that helps.

When I worked it out, I got the same answer as the OP but I realize this is incorrect. I'm assuming they fell into the same mistake I did. I worked out the stoichiometry problem like you did.

$1 x 7 drachma/$1 x 3 quilo/5 drachma

My problem was the above way I wrote it.

I'm having an issue in thinking that the units should cancel out here. In the problem I laid out, they do. In your example, dollars do not cancel out as they are both in the numerator for the first problem.

How do you explain setting that up? I realize you did it right but according to canceling units out, it is wrong so how do we justify it?

Basically, the way I did it, I made the dollar units NOT cancel out so that the final answer was in the form of $/quilos. The only currency I wanted to cancel out was the drachma because in the final solution you only wanted to compare $ to quilos. Not sure if that helps. The question is kind of like solving for something like speed where you want it in miles per hr so you have to be careful to not to cancel out either miles or hrs. Let me know if that doesn't make sense.

+1 Thank you guys. Now I understand the way for solving this problem, but still don't understand why my calculation has different answer, logically it should be same. I used the chemistry stoichimetrical way as follows.
($1/7d ) x (5D/3Q) D cancel out and what we have left is $5/21Q which means $5 to 21Q ratio.

+1 Thank you guys. Now I understand the way for solving this problem, but still don't understand why my calculation has different answer, logically it should be same. I used the chemistry stoichimetrical way as follows.
($1/7d ) x (5D/3Q) D cancel out and what we have left is $5/21Q which means $5 to 21Q ratio.

I think what you need to do is take it one step further. You have the ratio of $5/21Q. This is the same as 5$:21Q. Now, you want the ratio of 1 dollar to x drachmas, so you divide each side by 5. This gives you 1$:21/5 drachmas. Does that clear it up?