Question

Sobre una recta se toman los puntos consecutivos P, A, B, C y D de modo que:
7PC = 2PD + 5PB y 2AD + 5AB =7
Calcula AC

Answer 1

$7pc = 2pd + 5pb \\ 2ad + 5ab = 7$
$\frac{p(2d + 5b)}{7p} = \frac{2d + 5b}{7} = c$

$a(2d + 5b) = 7 \\ \frac{7}{(2d + 5b)} = a$


AC
$( \frac{7}{2d + 5b} )( \frac{2d + 5b}{7} ) = \frac{7(2d + 5b)}{7(2d + 5b)} = 1$