Some students planned a picnic.

Solution:

Let x students planned a picnic.

Then, the share of each student $=\frac{480}{x}$

According to question, 8 students fail to go picnic, then remaining students $=(x-8)$.

Therefore, new share of each student $=\frac{480}{x-8}$

It is given that

$\frac{480}{x-8}-\frac{480}{x}=10$

$\frac{480 x-480(x-8)}{(x-8) x}=10$

$\frac{3840}{(x-8) x}=10$

$10\left(x^{2}-8 x\right)=3840$

$\left(x^{2}-8 x\right)=384$

$x^{2}-8 x-384=0$

 

$x^{2}+16 x-24 x-384=0$

$x(x+16)-24(x+16)=0$

$(x+16)(x-24)=0$

Because x cannot be negative.

Thus, the total numbers of students attend a picnic

$=x-8$

$=24-8$

$=16$

Therefore, the total numbers of students attend a picnic be $x=16$