Question

Question #3770d

Answer 1

I suspect there may be something wrong with this question.
I have invited someone specific to look at this question.

Explanation:

`color(blue)("First interpretation of the question: This one fails")`

The total count of the 'sample population' we are considering is

`2/3+2/5` of the whole `= [(2xx5)/(3xx5)]+[(2xx3)/(5xx3)] = 10/15+6/15`

`= 16/15` of the whole

Note that you can not have more people with lunch than there are people in the whole. `color(red)("Consequently this model is wrong")`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Second interpretation of the question: This one should work")`

`color(green)("Of the people that brought lunch ("2/3" of the whole) ")`
`color(green)(2/5" bought lunch")`

Proportion(1)
So `2/5xx2/3=5/15` of the whole population paid for their lunch

Proportion(2)
So those that did not pay for their lunch is

`(1-2/5)xx2/3= 2/5=6/15` of the whole population.

The proportion that did not pay for their lunch is higher than those that did. As implied in the question.

The ratio for this is
`"did not pay : paid" ->6/15:5/15`

Presenting the ratio in `color(red)("fractional FORMAT")`

`("did not pay")/("paid")->6/5color(red)(" note that ratio is not a fraction")`

As a fraction we have `6/(6+5) = 6/11` did not pay

As a fraction we have `5/(6+5)=5/11` did pay

So complying with the wording requirement of the question we have:

`6/11-5/11=1/11` more of the student brought (did not pay)