Question

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?

Answer 1

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`