Question

Mia needs to separate 270 blue pens and 180 red pens into packs. Each pack will have the same number of blue pens and the same number of red pens. What is the greatest number of packs she can make? How many red pens and how many blue pens will be in each pack?

Answer 1

we know that

$270=2*3^{3} *5\\180=2^{2}*3^{2}*5$

Find the Greatest Common Factor (GCF)

The GCF is equal to------> $2*3^{2}*5=90$

therefore

the answer part a) is

the greatest number of packs she can make is $90$

Find the number of red pens in each pack

Divide the total number of red pens by the total number of packs

$\frac{180}{90}=2\ red\ pens$

Find the number of blue pens in each pack

Divide the total number of blue pens by the total number of packs

$\frac{270}{90}=3\ blue\ pens$

therefore

the answer part b) is

There are $2\ red\ pens$ in each pack

There are $3\ blue\ pens$ in each pack

Answer 2

Blue 90 pens in each pack
and 90 red in each pack