5. On one of two parallel lines, there are 8 points. How many points are on the other line if all the points together determine 640 triangles?

Each task is scored out of 10 points.

The use of a pocket calculator or any reference materials is not allowed.
first method):

$x^{2}+16 x-10 x-160=0$

$x \cdot(x+16)-10 \cdot(x+16)=0$

$(x+16) \cdot(x-10)=0$

2 POINTS

From $x+16=0$ we get $x_{1}=-16$, and from $x-10=0$ we get $x_{2}=10$.

1 POINT

Since the number of points must be a natural number, there are 10 points on the second line.

1 POINT

TOTAL 10 POINTS

Note 1: The equation $x^{2}+6 x-160=0$ can also be solved in the following two ways:

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