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

Answer:

16 colored pencils.

Step-by-step 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 $\frac{4}{5}x$ pencils.

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

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

$x+\frac{4}{5}x+\frac{3}{5}x=96$

$\frac{5}{5}x+\frac{4}{5}x+\frac{3}{5}x=96$

$\frac{5+4+3}{5}x=96$

$\frac{12}{5}x=96$

$\frac{5}{12}\times \frac{12}{5}x=96\times\frac{5}{12}$

$x=8\times5$

$x=40$

Now, we will subtract $\frac{3}{5}x$ from x of 40 as:

$x-\frac{3}{5}x$

$40-\frac{3}{5}(40)$

$40-3(8)$

$40-24=16$

Therefore, Samantha has 16 fewer colored pencils than Morris.