Question

Marvin has 4 books to read for homework this week. If he reads 2/3 of a book each night, how many nights will it take him to read all four books?

Answer 1

`6` nights

Explanation:

Since it takes Marvin one night to `2/3` of a book, then you can think of it as

Book:Night
`2/3:1`

`4`: `x`

`x=(4times1)/(2/3)`

`x=4times3/2`

`x=6`

therefore, it would take 6 nights for Marvin to finish 4 books

Answer 2

If he reads `2/3` of a book in `1` night, then he'll read `4/3` of a book in 2 days.

`2/3x=y`

`color(white)(.....) x color(white)(..) | color(white)(..) y`
`color(white)(.)* * * * * * * *`
`color(white)(.....) 1 color(white)(..) | color(white)(..) 2/3`

`color(white)(.....) 2 color(white)(..) | color(white)(..) 4/3`

`color(white)(.....) 3 color(white)(..) | color(white)(..) 2color(white)(/x)`

`color(white)(.....) 4 color(white)(..) | color(white)(..) 8/3`

`color(white)(.....) 5 color(white)(..) | color(white)(..) 10/3`

`color(white)(.....) 6 color(white)(..) | color(white)(..) 4color(white)(/x)`

So, according to this table, if he reads `2/3` of a book a night, he will finish `4` books in `6` days

We could also have solved this using an equation:

`2/3x = 4`

`x = 4 xx 3/2`

`x = 12/2`

`x=6`

Answer 3

6 nights

Explanation:

Using ratio but in fraction format (this is not a fraction!!!!!)

Let the unknown time measured in nights be `t`

`("count of books read")/("time in nights") color(white)("dd")-> color(white)("dd")(color(white)(..)2/3color(white)(..))/1 = 4/t`

There is a mathematical way of doing this but I am just going to say: turn EVERYTHING up the other way giving:

#("time in nights")/("count of books read") color(white)("dd")-> color(white)("dd")(color(white)(..)1color(white)(..))/ (2/3) = t/4#

Multiply both sides by 4

`(color(white)(..)(1xx4)color(white)(..))/(2/3) =t`

`t=4xx3/2`

`t=4/2xx3`

`t=2xx3=6" nights"`