Math Destroyer 2010 Test 7, Quesiton 11

[Canard]

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The quesiton asks:

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?

I thought it was just simple calculation like this:

($1/7 drachmas)*(5drachmas/3quilos) = $5/21quilos --> therefore the ratio of dollar to quilos which is (dollar)/(quilos) is 5/21

but the answer says 21/5, I am confused if I am wrong or the solution is? If anybody can make sense of this, it will help alot, thanks

 

[dentalWorks]

 

[herkulease]

this is one of those questions that all depends on how you read the question.

Its a question I don't believe will show up. Your answer is technically not wrong. It a semantics one. what he is really asking for is 1 dollar gets you how many quilos.

It is similar to exchange rates you find in the paper or online. It is told you that 1 US Dollar = X amount in foreign currency. Its incredibly rare to see 100 usd or any other amount unless the number is so small. The way he phrased the question makes both answers perfectly valid imo.

Here's why I think there are two valid answers.

the answer of 5/21 tells us that 5 US dollars = 21 quilos.

the answer of 21/5 tells us that 1 US dollar = 21/5 quilos.

This is similar to saying 1 foot = 12 inches, and 5 feet = 60 inches. It is just that normal convention in terms of money tells you to do 1 dollar = X amount and that how he gave his answer.

If you're travel a lot, sometimes the 1 dollar = X foreign currency just doesn't work. Its some odd amount that you can't get(country may not have such a denomination)

 

[Canard]

thanks for the help.

I understand what you are saying that in $1, there are 21/5 quilos but....

Maybe it is just me and not being able to understand but when a question asks "what is the ratio of dollars to quilos" then shouldn't the fraction form of the ratio should be dollar/quilos? and not quilos/dollar ???

 

[dentalWorks]

actually now that I think about it... as long as you specify the units... both answers are correct.

5$ / 21D is correct and so is 21D / 5$

Just like 12 inches = 1 foot..... 1 foot = 12 inches

 

[spoog74]

actually now that I think about it... as long as you specify the units... both answers are correct.

5$ / 21D is correct and so is 21D / 5$

Just like 12 inches = 1 foot..... 1 foot = 12 inches

No, i dont believe that 21 D/ 5$ is correct for that question. The question SPECIFICALLY asks for DOLLARS TO QUILOS which i believe should be 5 / 21

 

[Bombidillo]

this is one of those questions that all depends on how you read the question.

Its a question I don't believe will show up. Your answer is technically not wrong. It a semantics one. what he is really asking for is 1 dollar gets you how many quilos.

It is similar to exchange rates you find in the paper or online. It is told you that 1 US Dollar = X amount in foreign currency. Its incredibly rare to see 100 usd or any other amount unless the number is so small. The way he phrased the question makes both answers perfectly valid imo.

Here's why I think there are two valid answers.

the answer of 5/21 tells us that 5 US dollars = 21 quilos.

the answer of 21/5 tells us that 1 US dollar = 21/5 quilos.

This is similar to saying 1 foot = 12 inches, and 5 feet = 60 inches. It is just that normal convention in terms of money tells you to do 1 dollar = X amount and that how he gave his answer.

If you're travel a lot, sometimes the 1 dollar = X foreign currency just doesn't work. Its some odd amount that you can't get(country may not have such a denomination)

I agree with this post. I am bumping this since I also had issues with it and perused the internet for an answer.

What it comes down to: poor wording and non-specific answers. It's asking for a ratio of a to b, which is of course a:b or a/b

If you do this the purely mathematical way to get $/Q you will get 5/21 which means 5:21 or 5 dollars per 21 quillos. This is a valid ratio. However, if you want to know how many quilos are in one dollar then 1 dollar is 5/21 quilos. All you did here was take 5:21 and then divide it by 5 on each side.

In my semantic opinion, the destroyer gives you the wrong answer. My reason for this is the following: If you want to find how many quilos are in one dollar, then the mathematical ratio is technically quilos to dollars or "quilos per dollar" which inverts the ratio by definition.