# QR DAT destroyer question

#### 299678

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?

Answer is 21/5, but my calculation is 5/21

is this wrong answer for destroyer or me

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?

Answer is 21/5, but my calculation is 5/21

is this wrong answer for destroyer or me
I think you just got confused with the term "dollars to quilos".
So you want to get dollars/quilos right?
so let's set up the equation:

1 dollar= 7 Drachmas ---eq.1
5 Drachmas = 3 Quilos --eq.2

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

#### Maygyver

10+ Year Member
5+ Year Member
You can do this also by just setting up this:

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.

#### dentalpath

##### Dental Student
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)

#### Avery07

10+ Year Member
7+ Year Member
You can do this also by just setting up this:

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?

#### Maygyver

10+ Year Member
5+ Year Member
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.

#### herkulease

10+ Year Member
I looked at this problem its in how you read the question that might lead to confusion and the fact that the answer choices has both 21/5 and 5/21.

I read the question as asking for 1 dollar equals how many quilos does Alfred get. This is the traveler in me.

But reading it that way you can setup two equations.

1U = 7D and 5D = 3Q.

You can solve and find that D = 3/5Q

plug that back in the the 1st question and you'll get 1U = 21/5Q

if we do it like stoichiometry for gchem like maygyver set it up it would be 5 dollars/ 21 Quilos.

mine and destroyers way is 1 dollar to 21/5 quilos

both end up resulting in the same for Alfred, his 1 dollar would equal 4.2 quilos.

#### 299678

+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.

#### Maygyver

10+ Year Member
5+ Year Member
+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?