Question

In college, summer vacation is five days more than 5 times the length of winter break. Spring break is one-third as long as winter break. If winter break is r days long, how many days off do college students receive for the three breaks?

Answer 1

`19/3r+5` days

Explanation:

If r equals the number of days for winter break then the length of summer break is
`5r+5`

and the length of spring break is
`1/3 r`

To get the total number of days, add all three together to get
`r + (5r +5) + 1/3r`
`19/3r+5`

Since there are no numerical values expressed the value in days can not be found.

Answer 2

`color(purple)("A demonstration on how to build an equation(s) from a word question.")`

You can only express this in terms of `r ->6 1/3r+5`

This is the same as: `19/3 r+5`

Explanation:

Breaking the question down into its component parts:

Let summer break be `.S_u larr` (my own permanent notation)
Let spring break be `....S_p larr` (my own permanent notation)
Let winter break be `....w color(white)(.)larr` (my temporary notation)

Summer vacation is `...........->S_u=?`
5 day more than`..................->S_u=?+5`
5 times `.............................->S_u=5?+5`
the length of winter break `..->S_u=5w+5 " ".....Equation(1)`

Spring break is `->S_p=?`
one third `........->S_p=1/3`
as long as `.....->S_p=1/3?`
winter break `..->S_p=1/3w" "..................Equation(2)`

If winter break is `r` days long `=>` substitute `r` for `w`

`S_u=5r+5 " "...........Equation(1_a)`
`S_p=1/3r" "..................Equation(2_a)`

If declared in the question you must use the notation they define.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The total days of expressed in terms of `r`

Winter `......w-> color(white)(.....)r`
Spring `......S_p->color(white)(..)1/3r`
Summer `..S_s->color(white)(....)ul(5r+5) larr" add"`
`" "6 1/3r+5`