1

So me and a mock test creator were having this discussion about one of his problems. Here it is:

In shrom currency, $\frac37 \text{ shrims}$, $4 \frac57\text{ shrums}$, and $14 \frac17\text{ shrams}$ have the same value. How many shrums are in one shram and one shrim? Express your answer as a mixed number.

So what I did was this: Take shrims and shrums, and multiply by $\frac73$ to get $1\text{ shrim} = 11 \text{ shrums}$. Do the same for shrums and shrams to get $1\text{ shram} = \frac13\text{ shrums}$.

What the test creator did was this: Let $\text{shrim} = 77$. Then, $\text{shrum} = 7$ and $\text{shram} = \frac73$. So, $1\text{ shrim} = \frac1{11}$, and $1\text{ shram} = 3$.

$11 \frac13$ vs $3 \frac1{11}$. Who is right? I don't see anyhting wrong with either, and it gives me a headache just thinking about it.

Alain Remillard
  • 3,625
asdf334
  • 376

1 Answers1

1

You are right. The test creator did a mistake in the last step.

If the value of each currency is, as the test creator found,

  • $1 \text{ shrim}=77$;

  • $1 \text{ shrum}=7$;

  • $1\text{ shram}=\frac73$

then it takes $11\text{ shrums}$ to make a shrim, and it takes $3\text{ shrams}$ to make a shrum.

Hence $1\text{ shrim}$ and $1\text{ shram}$ is equal to $11\frac13\text{ shrums}$.

Alain Remillard
  • 3,625