Emilio has 189 books to put onto 9 shelves. Some shelves hold 15 books and others hold two dozen. How many of each size shelf will Emilio use?

1 Answer
Mar 13, 2018

Answer:

15 book content shelf count #=3#
24 book content shelf count #=6#

Explanation:

This is a 'blending' of different materials type problem

Total count of shelves is 9
Total count of books is 189

Let the count of shelves for 15 books be #x#
Then the count for 2 dozen books is #9-x#

Total count of books on the shelves is:

#"Blend type 1"color(white)("d")+color(white)("d")"Blend type 2"#
#color(white)("ddd")15xcolor(white)("ddddd")+color(white)("dd")24(9-x)color(white)("dd")=189#

#15x-24x+216=189#

#216-189=24x-15x#

#27=9x#

#x=3#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
15 book content shelf count #=x=3#
24 book content shelf count #=9-x=6#