The number of large boxes is 4 and the number of small boxes is 14.
Explanation
Suppose, the number of large boxes is [tex]x[/tex] and the number of small boxes is [tex]y[/tex]
As, the total number of boxes is 18, so the first equation is....
[tex]x+y= 18 .......................................(1)[/tex]
The large boxes hold 35 books, and the small ones hold 20 books and the total number of books is 420. So the second equation will be .....
[tex]35x+20y=420................................(2)[/tex]
Now solving equation (1) for [tex]y[/tex] itself , we will get....
[tex]y= 18-x[/tex]
We will plug this [tex]y= 18-x[/tex] into equation (2). So.....
[tex]35x+20(18-x)=420\\ \\ 35x+360-20x=420\\ \\ 15x= 420-360\\ \\ 15x=60\\ \\ x= \frac{60}{15}=4[/tex]
Now plugging this [tex]x=4[/tex] into the equation [tex]y= 18-x[/tex].......
[tex]y= 18-4= 14[/tex]
Thus, the number of large boxes is 4 and the number of small boxes is 14.
