Fraction question

[Bringlebubble]

Hello I’m new here and I was hoping someone could offer me some help as I’m really stuck on this fraction problem.
last year Jeremy had two jobs. As a waiter he earned £90 per weekend for 26 weekends. As a driving instructor he earned £720 a week for 13 weeks. What fraction of his total income was from being a waiter. Give your answer in the simplest form. I keep coming out with 1/9 which isn’t correct.
Thanks in advance.

 

[Dr.Peterson]

Hello I’m new here and I was hoping someone could offer me some help as I’m really stuck on this fraction problem.
last year Jeremy had two jobs. As a waiter he earned £90 per weekend for 26 weekends. As a driving instructor he earned £720 a week for 13 weeks. What fraction of his total income was from being a waiter. Give your answer in the simplest form. I keep coming out with 1/9 which isn’t correct.
Thanks in advance.

Please show us how you got 1/9. I can't see a way to get that, so I can't tell you what error you are making.

In particular, what do you get for the total income, and how?

 

[JeffM]

I hate problems like this because they are ambiguous.

What period does the total income income refer to, the period of 13 weeks when he may have had two jobs, or the period of 26 weeks when he may have had only the weekend job, or the entire year? The entire problem depends on what period we are referring to and to what extent the different jobs were coincident in time.

I can get an answer of 1/9 if we assume that we are asking about a period of 13 weeks during which Jeremy had both jobs. If we are asking about some other period or if there was no period of weeks when Jeremy had both jobs simultaneously, then we get different answers.

If students learn nothing else from mathematics, they should learn the importance of formulating questions clearly.

 

[Mr. Bland]

I hate problems like this because they are ambiguous.

Except this one isn't ambiguous.

It's asking about the percentage of total income for the entire year, not for any particular span of time when Jeremy may or may not have been working both jobs simultaneously.

Jeremy made [MATH]£90 * 26[/MATH] as a waiter and [MATH]£720 * 13[/MATH] as a driving instructor. This is a simple fraction problem:

[MATH]\frac{waiter}{total} = \frac{90 * 26}{90 * 26 + 720 * 13}[/MATH]​

I don't see any other way to interpret this.

 

[Steven G]

And the math is easy. [math]\dfrac{90*26}{90*26 + 720*13} = \dfrac{90*26}{180*13 + 720*13} = \dfrac{90*26}{900*13} = ...[/math]

 

[JeffM]

Except this one isn't ambiguous.

It's asking about the percentage of total income for the entire year, not for any particular span of time when Jeremy may or may not have been working both jobs simultaneously.

Jeremy made [MATH]£90 * 26[/MATH] as a waiter and [MATH]£720 * 13[/MATH] as a driving instructor. This is a simple fraction problem:

[MATH]\frac{waiter}{total} = \frac{90 * 26}{90 * 26 + 720 * 13}[/MATH]​

I don't see any other way to interpret this.

Where is the word “annual”?

 

[Dr.Peterson]

Where is the word “annual”?

It's asking about the "total income", which clearly must refer to "last year", since that is what the entire question is about. The word "annual" is not needed.

I'd call the problem only slightly ambiguous, and then only to picky people like us. The proper method of interpretation is to take the meaning under which the problem makes sense, giving all the required information.

 

[JeffM]

It's asking about the "total income", which clearly must refer to "last year", since that is what the entire question is about. The word "annual" is not needed.

I'd call the problem only slightly ambiguous, and then only to picky people like us. The proper method of interpretation is to take the meaning under which the problem makes sense, giving all the required information.

Actually, it is quite obvious that this student entirely missed that interpretation. He seems to have interpreted “total” as meaning from both jobs and pertaining to a week or a quarter.

[MATH]\dfrac{90}{720 + 90} = \dfrac{90}{810} = \dfrac{1}{9}[/MATH] Perfectly sound arithmetic.

I agree that interpreting “total“ in conjunction with “last year” makes sense, but it is not the only possible construction. The student is being taught arithmetic rather than a canon for construing English prose. “Total annual income” precludes the need for trying to deduce what was the intent. People who are writing problems to teach arithmetic (or elementary algebra) need to remember that their audience does not consist of people like me who have read thousands of drafts of legal documents looking for ambiguities or of PhDs, who have had to struggle through tomes of dense prose. We are experts at interpreting documents; few 11 year olds are.