Question

Samantha has 3/4 as many colored pencils as Carl Carl has 4/5 as many color pencils as Maurice if they have 96 colored pencils altogether how many fewer colored pencils does Samantha have the Morris

Answer 1

16 colored pencils.

Explanation:

Let x represent the number of pencils that Maurice has.

We have been given that Carl has 4/5 as many color pencils as Maurice, so Carl have
`(4)/(5)x` pencils.

We are also told that Samantha has 3/4 as many colored pencils as Carl, so Samantha would have
`((4)/(5)x)\cdot (3)/(4)=(3)/(5)x` pencils.

Since have 96 colored pencils altogether, so we will equate sum of all pencils with 96 as:

`x+(4)/(5)x+(3)/(5)x=96`

`(5)/(5)x+(4)/(5)x+(3)/(5)x=96`

`(5+4+3)/(5)x=96`

`(12)/(5)x=96`

`(5)/(12)* (12)/(5)x=96*(5)/(12)`

`x=8*5`

`x=40`

Now, we will subtract
`(3)/(5)x` from x of 40 as:

`x-(3)/(5)x`

`40-(3)/(5)(40)`

`40-3(8)`

`40-24=16`

Therefore, Samantha has 16 fewer colored pencils than Morris.