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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?

? children

? notebooks

Respuesta :

4 children
60 notebooks 

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

Explanation

Lets assume, Mama has [tex] x [/tex] number of children and [tex] y [/tex] number of notebooks.

If she give 13 notebooks to each of her children, then 8 books are left. So,

[tex] y=13x+8 ...............................(1) [/tex]

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

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

[tex] 13x+8=15x\\ \\ 13x-15x= -8\\ \\ -2x= -8\\ \\ x=\frac{-8}{-2}=4 [/tex]

Now, [tex] y=15x=15(4)=60 [/tex]

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


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