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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?

Respuesta :

dannielle
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

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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