Question

Mama had several notebooks. If she give 13 notebooks to each of her children, she will have 8 left. If she give 15 notebooks to each of her children, she will have nothing left. What is the smallest number of notebooks and children does mama have?

Answer 1

N= 13*c+8
n=15*c
15c=13c+8
15c-13c=8
2c=8
c=8:2
c=4 children
n= 15*4=60 notebooks

Answer 2

The number of children is 4 and the number of notebooks is 60.

Explanation

Lets assume, Mama has $x$ number of children and $y$ number of notebooks.

If she give 13 notebooks to each of her children, then 8 books are left. So, $y= 13x +8 ..................................(1)$

And If she give 15 notebooks to each of her children, she will have nothing left. That means $y= 15x .....................(2)$

Now solving the system of equations, we will get ....

$13x+8 = 15x \\ \\ 13x-15x = -8 \\ \\ -2x = -8\\ \\ x= \frac{-8}{-2}= 4$

Now, $y= 15x = 15(4)= 60$

So, the number of children is 4 and the number of notebooks is 60.