Question

John is packing books into boxes to send to his cousins in case they are snowed in and want to do some light reading. Each box can hold either 15 small books or 8 large books. He needs to pack at least 35 boxes and at least 350 books. Write a system of linear inequalities to represent the situation

Answer 1

`x+y \geq 350` ... I

`(x)/(15)+ (y)/(8) \geq 35` ... II

Explanation:

Given that John is packing books into boxes to send to his cousins in case they are snowed in and want to do some light reading.

Let x represent the number of small books and y the number of large books.

The box capacity is either 15 small books or 8 large books

i.e. we have
`15x = 8y`

No of books is atleast 350 and no of boxes he needs is atleast 35

Total no of books =
`x+y \geq 350` ... I

is the first inequality

Next is he wants 35 boxes.

One box can hold either 15 small books or 8 large books.

For x books no of boxes required = x/15 and for y book no of boxes is y/8

Total no of boxes is atleast 35

`(x)/(15)+ (y)/(8) \geq 35` ... II