Question

It's moving day, and Lydia has packed her books into large and small boxes. The large boxes hold 35 books, and the small ones hold 20 books. She packed her 420 books into 18 boxes. How many are large, and how many are small?

Answer 1

The number of large boxes is 4 and the number of small boxes is 14.

Explanation

Suppose, the number of large boxes is $x$ and the number of small boxes is $y$

As, the total number of boxes is 18, so the first equation is....

$x+y= 18 .......................................(1)$

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 .....

$35x+20y=420................................(2)$

Now solving equation (1) for $y$ itself , we will get....

$y= 18-x$

We will plug this $y= 18-x$ into equation (2). So.....

$35x+20(18-x)=420\\ \\ 35x+360-20x=420\\ \\ 15x= 420-360\\ \\ 15x=60\\ \\ x= \frac{60}{15}=4$

Now plugging this $x=4$ into the equation $y= 18-x$.......

$y= 18-4= 14$

Thus, the number of large boxes is 4 and the number of small boxes is 14.